as a function of price. Determine the dance committee's greatest possible revenue. Notice that the result is a quadratic equation. Direct link to ballacksecka55's post sal am totally confuse ev, Posted 5 years ago. I D d Direct link to Caleb Reardon's post This question can be answ, Posted 4 years ago. YES, u can skip it and attempt it in the last if u want 800. 200 times P minus $9.30. $ we can distribute this P and we're gonna get income The max revenue will occur when you lower the rent to $300 - 5(10) = $250 and the max revenue will be About the Author. halfway between zero and this, halfway between zero and that. Expression a quadratic function in three different forms: standard, vertex, and factored; Finding a quadratic function given three distinct points on its graph; Finding a function to model a real-life parabola; Solving quadratic equations algebraically and graphically; Solving real life problems by creating and using quadratic models 3 " ` ? MAXIMIZING REVENUE WORD PROBLEMS INVOLVING QUADRATIC EQUATIONS Problem 1 : A company has determined that if the price of an item is $40, then 150 will be. times with 26 left over. To cancel out .10, you need to multiply 20 by the reciprocal of .10, which is 10. Answer: Profit is the difference between the amount of money made, called revenue, and the costs involved in making that money. You will need to use keywords to interpret the English and, from that, create the quadratic model. when 275 units sold, we can get the maximum revenue. (a) Let x the number of sandwiches and y be the cost per sandwich. $9.30, this would give us the absolute price increase, the price per subscriber, times the price per subscriber. MAXIMIZING REVENUE WORD PROBLEMS INVOLVING QUADRATIC EQUATIONS Problem 1 : Solution : = (-10x + 550) x R(x) = -10x2 + 550x (c) To find the number of. ? Direct link to camilo parets's post after rewatching this vid, Posted 2 years ago. I really love how it understands my handwriting too, genuinely has helped me as a student understand the problems when I can't understand them in class, this app is constantly helping me throughout my mathematics problems This app deserves 5 stars . Direct link to Vivek Nair's post At 2:42, how is 20 divide, Posted 8 years ago. (d) At what price is the company selling the cameras at when the revenue is maximized? KA?H1 : aM,,He` @201d++&1X +|-?TT W-L$$bbI9W8|a# 5y;m'^Fn6 p{|@ *, 2023 by HEAD OF THE CLASS. So let's think a little We have 2400 subscribers. How many items does the company have to sell each week to maximize profit? A ball is shot from a cannon into the air with an upward velocity of 40 ft/sec. Halfway between your two roots are when you hit the maximum point, so that's another way that 10) A projectile is fired from a cliff 200 feet above the water at an inclination of EMBED Equation.DSMT4 to the horizontal, with a muzzle velocity of 50 feet per second. x\Ys3qNpNRvJSe'$-Svv) Fifc/w_W? for a sandwich in order to maximize its revenue. You can find the x-values that Choose an expert and meet online. 5 M T W ` a h j " # % } 1 6 h h h h : h/ j h_> h_> EHUjFI There are several standard types: problems where the formula is given, falling object problems, problems involving geometric shapes. So at the current price, l"1X[00Yqe6 Get Help is here to help you with whatever you need. Direct link to raima.hossain's post I am really confused abou, Posted 2 years ago. Just find the vertex. That's $10.65. to be the maximum point. h/ CJ UVaJ j! Both are set up almost identical to each other so they are both included together. So you get 4,260 minus 200 P. So we now have a simplified subscribers as a function of price, and now we can substitute Quiz & Worksheet Goals. This app is amazing and a life saver. You are managing a 1600 unit apartment complex. t Ekh!&f2yd^(Qw"-Zi[g 6=NWy*Dc||9i{? D d So plus 1860, that's negative Extra Prractice quadratic word problems section 1.1 thru 1.4. Determine whether the graph has a maximum value or a minimum value. So let's multiply that, The rocket will fall into the lake after exploding at its maximum height. Most questions answered within 4 hours. 3 " ` ? (Hint: express the product as a function of x) 3) Among all rectangles that have a perimeter of 20 feet, find the dimensions of the one with the largest area. This PDF provides a full solution to the problem. Similar to above question, the maximum of the revenue would be at (-b/2a) i.e. " times negative $9.30, let's see, that's going @6O0u+]bD>D1PQEY ovI D d (d) At what price is the company selling the cameras at when the revenue is maximized? c $ A ? h3 CJ UVaJ j h3 Uh3 h : 5CJ aJ h 5CJ aJ hC! 5CJ aJ hJ hJ 5CJ aJ $ % & ! Find the roots: r2 12r 35 0 2. hc CJ UVaJ j hc Uhc h h/ j, h_ h/ EHUjJ* h_ h/ EHUjW gO A positive number x and its reciprocal are added together. HSF.IF.B.4. Step 4: Set each factor equal to 0, and solve for the two x-intercepts (roots/zereos). over 2 times negative 200, so that's gonna be negative 400. Maximum revenue word problems worksheet - MAXIMUM PROFIT WORKSHEET KEY. you can then substitute back in here and then you're writing S, we can write, we can write 4260 minus 200 P and then times P, times P. Now we can distribute, Quadratic Word Problems.notebook. But we're going to lose 20 subscribers, so lose, so I'm gonna (c) We should find the number ofsandwiches to be sold out to maximize the revenue. 1. y= 4x2 56x+96 The revenue equation based on the survey is R = (500 - 10x) (20 + 1x). And let's see, can I simplify this? Once they are set up, we will solve them in exactly the same way we solved the Find the maximum revenue Luci can make selling cookies in one day. To solve a math equation, you need to find the value of the variable that makes the equation true. (10.3.1) - Solve application problems involving quadratic functions Objects in free fall; Determining the width of a border; Finding the maximum and minimum values of a quadratic function . (p 3!Dl'/oR1HFQb ?QAj;6.A4w:>\WrZ/ZZYu\jJa9$Def?z3\y,]jjV]&b3cJSuJ;'A|=m5,`XOM'7LOLwL5fY2 E4 A]'ugF`iH|j^_e[6O(oFmfJfB1D>[E9Qdwi D d (d) What is the price of each item when maximum revenue is achieved ? Solution: Profit equals revenue less cost. Check out our website for a wide variety of solutions to fit your needs. problems: if you want to minimize the square root of a quadratic, that's the same as making the quadratic as small as possible. so negative b is 4260. Lesson 4 - Properties of Quadratics. 9) The price EMBED Equation.DSMT4 (in dollars) and the quantity EMBED Equation.DSMT4 sold of a certain product obey the demand equation EMBED Equation.DSMT4 EMBED Equation.DSMT4 . Page 6. The calculator uses the following formula: x = (-b D) / 2a, where D = b 2 - 4ac This formula calculates the solution of quadratic equations (ax 2 +bx+c=0) where x is unknown, a is the quadratic coefficient (a 0), b is the linear coefficient and c represents the equation's constant. hVn8> (.EPp'4Ig+7(iA%y. 5,X0cahadX9) qH2Or}D"<73E*x-=ggYh*+Wc]u84$&lIOf3SlbU<14b(JgiJ >-=&ygtFk:<3dqJnS3ZWiqAdm)r_-LF.ie$c2*YL*;uA9Hs*M6}ou^8mVD{P}w>rb~D{s}aKhgn~wF\6.nhF@'0d2aDDWZ'GY^2OjdUEw7`u$EY-0;@4][\ "Pi+ZLGS4A !%mTL6*BkJLFDZ1J8/|W}5glaeL+(.$BX0pC#S|'_MR7.\j{yYO1]?. If it was upward opening, Because the question says maximize we need to find the . Direct link to India Barrow's post don't we only get like 50, Posted 2 years ago. You might have to use common sense or other constraints in the problem to restrict the domain you're . price, and that makes sense. Oh, I'm going to be careful here. 1. %PDF-1.4 % # $ & ' ( ? P equals that is going to be when you hit the minimum or maximum point. Let's first take a minute to understand this problem and what it means. The height EMBED Equation.DSMT4 of the projectile above the water is given by EMBED Equation.DSMT4 where EMBED Equation.DSMT4 is the horizontal distance of the projectile from the face of the cliff. to be equal to 2400, and then, let's see, 20 divided by 0.1 is going to be 200 minus What is the maximum revenue? Find the price she should sell the cookies for to make the maximum revenue. Now in this little, in the problem, they tell us that the Maximizing Revenue Word Problems Involving Quadratic. The most difficult thing is interpreting the word problems into function, is there a easier way to do this? She found that the relationship between the price of a cookie, p, and the number of cookies sold, x, is given by the linear relationship EMBED Equation.3 . .0CZRc:lcYaqy(O7`l@mK-"-ohL_)%eB2$Zhx)nOhJof(q4AZL}B|">c9(f~@Y. Find the integers. h3 CJ UVaJ j h] h3 EHUj"'K where x = the number of $5 decreases in rent. b ]ks}v_%xx;n%v~F"a**?zU^yl2f] &u373 lqkPR So if we do that, we get income is equal to, instead of Example 10.7.6. 3 " ` ? going to be at 4260 over 400, which is exactly what The cost is $0.65 a loaf. Word Problems with Quadratic Functions Feb. 14, 2013 3 likes 28,064 views Download Now Download to read offline Education Mrs. LaPage Follow Advertisement Recommended Solving Word Problems Involving Quadratic Equations kliegey524 49.7k views 7 slides Quadratic equation word problems jchartiersjsd 11.4k views 1 slide "EU:8d\\PwA9'*-{> ) *Mh[(&i]s6O|u`BFdyv$l/*{~K'pLm Step 3: After the problem has been factored we will complete a step called the "T" chart. by five, 10 and 65/100, which is the same thing as $10.65. hbbd``b` $AC $ j $X4:'zb"@F_a`bdd100RDg\ "+ h/ CJ UVaJ jQ; h/ h/ EHUji!gO So this is probably the most interesting part of this problem. h_ CJ UVaJ j h_ Uh_ h3 # ! I need help in answering. Word Problems on Quadratic Equations: In algebra, a quadratic equation is an equation of second degree. $0.10 reduction in price, 40 more sandwiches will be sold. And so, if we wanted to write Direct link to teralynn.steele's post Why does he divide by .10, Posted 3 years ago. Its height, h, in feet, above the ground is modeled by the function h = -16t 2 + v 0 t + 64 where t is the time, in seconds, since the projectile was launched and v 0 is the initial velocity. a) Express the revenue R as a function of EMBED Equation.DSMT4 . And now we can add, we To do these. Check out our solutions for all your homework help needs! A common application of quadratics comes from revenue and distance problems. Currently, 800 units are rented at $300/month. The cost is $0.65 a loaf. The quantity of cellp. Our expert team is here to help you with all your questions. So let's see if we can write our number of subscribers ]-I?y~,N(9by wV@Q(/9.,4^\M`Mf}EW[h>J[d+!Q$*(~-`Qfe7En"3:Js D/kVFB{zj4;&?CA^up{2fF8 That's this price over here. c $ A ? Quadratic Functions Word Problems 1 1) The John Deere company has found that the revenue from sales of heavy-duty tractors is a function of the unit price that it charges. Since this is a maximum point, the x-coordinate gives the number of price increases needed to maximize the profit. ourselves how we can find the vertex of a parabola. The break-even point occurs when the total revenue equals the total cost - or, in other words, when the profit is zero. h/ CJ UVaJ h/ j h/ Uj h_ h/ EHU $ q r s 2 3 J K L M | } pc j5 hc hc EHUj#gO $ F % &. You can say, when does So subscribers is going To make money, let's assume that our business sells cellphones. j}V_el(biF4sNe @,/c(["6s D d 8 D if you need any other stuff in math, please use our google custom search here. What will the dimensions be? Looking for a way to get detailed step-by-step solutions to your math problems? SOLUTION: Maximum profit using the quadratic equations, functions, inequalities and their graphs. (c) Find the number of items sold that will give the maximum revenue. Because the question says maximize we need to find the vertex of R = (500 - 10x) (20 +, The vertex is located at (10, 250,000). Revenue Word Problem You are managing a 1600 unit apartment complex. L*: h-\IlD,J.=nc\p(S0D#['{F'"5(HQ-]/+-:|g l*':>d Y=p&|, D[q^ ExY8b/"Uuc/O ,g. b We offer 24/7 support from expert tutors. For example, in the sample problem above, it asks you to solve for the fare that will produce the maximum revenue. % Solve using the quadratic formula where a = 195, b = 20, and c = .21. d) Find the critical points (eliminate those not in the interval.) 8) The price EMBED Equation.DSMT4 (in dollars) and the quantity EMBED Equation.DSMT4 sold of a certain product obey the demand equation EMBED Equation.DSMT4 EMBED Equation.DSMT4 . What can you charge to earn a maximum revenue. c $ A ? Thanks you soo much. If a quadratic polynomial is equated to zero, then we can call it a quadratic equation. A market survey shows that for every 99 0 obj <>stream With a little perseverance, anyone can understand even the most complicated mathematical problems. c) What quantity EMBED Equation.DSMT4 maximizes revenue? What can you charge to earn a maximum revenue. as a function of price, is 4260 P minus 200 P squared. Price = independent variable and demand = dependent variable. Since the relationship between price and demand is linear, we can form a equation. Our team is dedicated to providing the best possible service to our customers. is you could say, look, if I have something of the z[/>_zo]{r0 V?[ HAZ7u2 5j0XG?Gsj1M5uj w/mK6J~VFupy3R{ gv.X+JW 7tZTogw|z4)fU!JZA]#rdYVNy? 2 AUczT5xq. `! AUczT5xq. U xT=hSQ>LDWvHcCiuI IcDb6! Get help from expert teachers to improve your grades. (d) How much should the deli charge for a sandwich in order to maximize its revenue ? . The numbers of sales decreases by $10$ times the numbers of times you increased the price: $300-10\cdot x$. Step 5: Use the formula: (r+s)/2, where r and s are the x-intercepts, to solve for the axis of symmetry. We know that because the coefficient on the second degree term is negative. subscribers themselves are going to be a function of Revenue = Quantity Demand Price ( Quantity). 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved, The Periodic Chart of Table of the Elements. c) At what horizontal distance from the face of the cliff will the projectile strike the water? -1 If you're looking for support from expert teachers, you've come to the right place. MPM2DI UNIT 6: QUADRATIC WORD PROBLEMS PART 4b SOLVING QUADRATIC WORD PROBLEMS - A RANDOM MIX - EXAMPLE Nancy walks 15 m diagonally across a rectangular field. $ ( 1 2 I J K L R S j k l m n o |te jW gO These questions are so hard, they should be illegal -_-. What is the smallest possible sum? ? 35,000 worksheets, games, and lesson plans, Spanish-English dictionary, translator, and learning. " of writing y and x, I wrote I and P, well, Our students test on average 78% betterthen nationwide averages on mathematical tests. .10=1/10, so the reciprocal is 10/1. 3 " ` ? This question can be answered using common sense by simply looking at the choices : Sometimes math can be surprising, it's best not to take chances unless your under extreme time pressure. MAXIMUM PROFIT WORKSHEET KEY. What is the maximum The quadratic function C (x) = a x 2 + b x + c represents the cost, in thousands of Dollars, of producing x items. At n=5; Revenue = 500 x 50 = 25000. )l; Plot y = Revenue is presented as the function of the projected decrease of price 84 0 obj <>/Filter/FlateDecode/ID[<2BA88866FC2ED24CA760502F6F44A532>]/Index[68 32]/Info 67 0 R/Length 82/Prev 147803/Root 69 0 R/Size 100/Type/XRef/W[1 2 1]>>stream stream Once you have found the key details, you will be able to work out what the problem is and how to solve it. make this function equal zero and then the vertex is going to be halfway between those points. is going to be equal to 10 and 13, 13, 13/20. So their income, let's h/ CJ UVaJ h : h h/ jZ h_ h/ EHUjW gO No packages or subscriptions, pay only for the time you need. 3 " ` ? b) Find the maximum height of the projectile. The revenue is maximal $1800 at the ticket price $6. Extra Prractice quadratic word problems section 1.1 thru 1.4. b Writing a quadratic function to model the revenue of a word problem and using it to determine the price of a product that with maximize the. going to be the vertex, this is going to be the P if you don't charge anything. and that makes sense. - YouTube 0:00 / 8:04 Maximizing Revenue Word Problem (Completing the Square): Straightforward. I am passionate about my career and enjoy helping others achieve their career goals. The first zero is 50010=50, and the second is -20. The manufacturer of digital cameras in Problem 11 has provided the, how do you make an equation for a trend line. Step 3: Create your equation for revenue in the form: Revenue= (Price)(Number of.). Max min revenue word problems - Step 1: Identify key information in the revenue word problem (Look above in the it asks you to solve for the fare that will . Step 3: Create your equation for revenue in the form: Revenue= (Price)(Number of). Then solve for the vertex, where the maximum or minimum value occurs. Average satisfaction rating 4.9/5. The revenue R is the product R = n*P, or R = n*(800-5*(n-100)) = 800n - 5n^2 + 500n = 1300n - 5n^2 = 5n*(260-n). Example 4: Find the formula for the revenue function if the price-demand function of a product is . Math can be tricky, but there's always a way to find the answer. h_ CJ UVaJ jt h_ h_ EHUj gO To get the maximum revenue, 1920 sandwiches to be sold out. need to figure out what price gets us to this maximum point, and this price, this is 231 068 959 solved problems. Step 4. Specify the domain of the function 7. (b) Find the revenue function. Currently, 800 units are rented at $300/month. Applications of quadratic functions word problems - Quadratic-based word problems are the third type of word problems covered in MATQ 1099, with the first. Looking for a resource that can provide detailed, step-by-step explanations? Step 4: Once ( ) are separated, set each ( ) = to 0 and solve for the variable. How do you set up, how So this graph, I as a function of P, so this is, if this, so if this is the I This question can be answered using common sense by simply looking at the choices : The first choice gives the option of $ 1.35 which will be too less as the costs won't be recovered. Your factory produces lemon-scented widgets. The grocer. Quadratic Word Problems.notebook. Well, let me just see, this is going to be 40 goes into 426 10 you can get the the decrease in the amount of subscribers for each 10 cent increase (for each choice ) then multiply the remaining amount with the the its selling cost. IT EVEN GIVES IN-DEPTH EXPLANATIONS AND GRAPHS! Look no further than our website. c $ A ? because if we subtract we get the amount that has been increased and once we divide with 0.1 we get how much it has been increased wrt 0.1 so we can directly multiply with 20 to see how many subscribers we have gained or lost)) if we repeat this process for 2 and 3 we see there is a slight profit for the third option.. The rocket's height above the surface of the lake is given by g(x)= . minus P is equal to zero. the easy way to think is as you can see you can cut out choice one and two also choice 4 (or you will have -subscription lol ). h_ h/ EHUj h_ h/ EHUj4 gO Kindly mail your feedback tov4formath@gmail.com, Graphing Linear Equations in Slope Intercept Form Worksheet, How to Graph Linear Equations in Slope Intercept Form. Economics: Marginal Cost & Revenue - Problem 1. Quadratic Optimization For problems 1 - 5, write the function. so if we just take our, if we take P minus B is this right over here, There's multiple ways to do it. What is the maximum revenue? A market survey has indicated that for each $5 you decrease the rent you will get by 20 new leases. ]| N^CszLKYlUR[{N+uf.F '7K/l~wz7|a^I|^V11o>dfm0}q'.gc.5f+$&9;?jfJ1Sb0xs rgif6Pc Yu''l d%*/T 2p nleNO~~qS{Uvz6j@`W}OMkkNY3]y8)Z7 QPcvqWT3 x/'I1ctj`~`gC\r-kV\2iM[1n9uA,=G?60hvv1L ?AhB)TtF'GgeqWE?,rb|P[ PFq>} jXY{IAB64[R(FP :mxIi{wgZx^) gG$ Knowing is the first step to understanding. 12. This quiz covers the following topics: Equation for the vertical position of an object in freefall as a function of time. 2 x = 13 + 5, so that 2 x = 18. And since you have no constant term, you actually can just factor a P, so you say, P times 4260 The max revenue will occur when you lower the rent to $300 - 5(10) = $250 and the . A company has determined that if the price of an item is $40, then 150 will be demanded So it's going to be 10 and 26/40, or we can write this as, this subscription price. First, the area of this rectangle is given by LW L W, meaning that, for this rectangle, LW = 50 L W = 50, or (W +5)W = 50 ( W + 5) W = 50. Determine the level/hours of . {-400/2(-40)} = 5. So that's going to be their income. negative of this coefficient, negative b over two times a. Proudly created with. Dividing by 2 gives x = 18 2 = 9. c) A number subtracted from 9 is equal to 2 times the number. Direct link to Revanth's post its actually super easy ,, Posted 3 years ago. Quadratic Word Problems Name_____ Date_____ T t2^0r1^4Q wKCuYtcaI XSdoYfKt^wkaprRen ]LULxCr.l c TAOlVlZ hrMiigQhTt^sV rr]eKsCeJrOv\exdh.-1-1) A fireworks rocket is launched from a hill above a lake. 68 0 obj <> endobj If the demand price is a linear function, then revenue is a quadratic function. % The best would be to get familiar all type of problems and keep practicing. Find the number of units, \displaystyle x, that a company must sell to break even if the profit equation is \displaystyle P(x)=500x-10,000. Quadratics - Revenue and Distance Objective: Solve revenue and distance applications of quadratic equa-tions. Find the vertex 2. hc CJ UVaJ jr2 hc hc EHUj#gO February 26, 2020. lose all your subscribers. It's the best math app I've seen. 6) A farmer has 3000 feet of fence available to enclose a rectangular field. xi\XT hrY hJ j h] h3 EHUj'K Then solve the model for the solutions (that is, the x -intercepts). This is going to be the same endstream endobj startxref The Calculus method is much more simple if you asked me.. same thing i was thinking. And so, what is that going to be? Find the maximum height attained by the ball. d) When the height of the projectile is 100 feet above the water, how far is it from the cliff? MAXIMIZING REVENUE WORD PROBLEMS INVOLVING QUADRATIC EQUATIONS Problem 1 : Solution : = (-10x + 550) x R(x) = -10x2 + 550x (c) To find the number of. Welcome to MathPortal. Unlike the typical ones. If you need help, our customer service team is available 24/7. Maximum Revenue Quadratic Word Problems. @ A B In this case, it's going stream Then interpret the variables to figure out which number from the vertex you need, where, and with what units. endstream endobj 69 0 obj <> endobj 70 0 obj <>/Rotate 0/Type/Page>> endobj 71 0 obj <>stream by consumers. 200 P is equal to zero. In many quadratic max/min problems, you'll be given the formula you need to use. Maximizing Revenue Word Problems Involving Quadratic. we have 2400 subscribers. Extra Prractice quadratic word problems section 1.1 thru 1.4.notebook 1 September 18, 2014 So you run a surf board shop. 5. subscription price. So we need to figure out, we Determine the number of subscribers needed for the publisher to break-even. The marginal cost function is the derivative of the total cost function, C (x). . Because once you do this, The math equation is simple, but it's still confusing. Direct link to Henry's post same thing i was thinking, Posted 8 years ago. But currently photos are not working but still amazing. First, add 5 to both sides. *Km\@3`=72 Step 6: Substitute your axis of symmetry value into the equation, based on what you are solving for. . That's the price at which you In Problems 1-6 nd the vertex, the maximum value, the minimum value, and the x-intercepts of the quadratic. 1. So you can say, when does 4260 P minus 200 P squared equal zero? 200 P is equal to zero. %PDF-1.4 So what's negative b? Let me show you what I'm talking about. Decide math If you need help, our customer service team is available 24/7. %PDF-1.4 5 xcdd``gd``ba V d,FYzP1n:&&! You decide that if you raise your price by $4, you will lose 12 clients. We solve this for x. 6. Or if 4260 minus P is equal to. Follow 1 coordinate of the vertex. The max revenue will occur when you lower the rent to $300 - 5(10) = $250 and the max revenue will be c`J2_u*Vh)`gRjjx&TR%HHAvS Bl=t^>Py3 |0|BkaWD([00~n c) What quantity EMBED Equation.DSMT4 maximizes revenue? 200 times negative 9.3. this expression in for S, in for S in our original equation. Day 4: Min & Max WORD PROBLEMS 1 A vertex is a maximum if the parabola opens down (a 0) The Real Deal: How to maximize the Revenue. "J@=$bBb|W]=h?(+e(bAl>da Based on a survey conducted, Direct link to tersooupaajr's post he did this incredibly sl, Posted 3 years ago. Philip P. sandwiches to be sold out to maximize the revenue. Solving projectile problems with quadratic equations Example: A projectile is launched from a tower into the air with initial velocity of 48 feet per second. revenue ? When the price is $45, then 100 items are demanded by consumers. after rewatching this video 3 times, i decided to skip this question, its actually super easy , essentially what you do is use the options itself to get the answer.. now first option is wrong obviously, the last one gives us negative subscribers (how?, well subtract 9.3 from it and divide it by 0.1 and then multiply it by 20 (why did we do that?
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