3. Suppose that SpryBorg Inc introduces a new computer game in Houston using tel

Question

3. Suppose that SpryBorg Inc introduces a new computer game in Houston using television advertisements. Surveys show that P% of the target audience buy the game after x ads are broadcast, satisfying 100 P(x)- 1+49e-013x What percentage buy the game without seeing a TV ad? (hint: what would x be times? problem? your results. (hint: first rewrite P(x) so that you don't have to use the quotient rule) a. ?) b. What percentage buy the game aft c. What do you notice as x gets larger? Does this make sense in the context of the d. Find the rate of change, P(x). Use this to find P5), P(s0), and P(90) Interpret er the ad is run 5 times? 20 times? 50 times? 60

Explanation / Answer

P(x) = 100 / ( 1 + 49 e-0.13x)

a) without seeing an ad means that there were no ads palyed, so x=0;
when x=0; P(x) = P(0) = 100/ (1+49*e0) = 100/(1+49) = 100/50 = 2
Thus, 2% would buy the game without seeing a TV ad;

b) if ad is run 5 times, x=5; P(5) = 100 / (1+49 e-0.13*5) = 100 / (1+49*0.522) = 100 / (26.578) = 3.76%
if ad is run 20 times, x=20; P(20) = 100 / (1+49 e-0.13*20) = 100 / (1+49*0.0742) = 100 / (4.6358) = 21.57%
if ad is run 50 times, x=50; P(50) = 100 / (1+49 e-0.13*50) = 100 / (1+0.0735) = 100 / (1.0735) = 93.153%
if ad is run 60 times, x=60; P(60) = 100 / (1+49 e-0.13*60) = 100 / (1+49*0.0004097) = 100 / (1.0200753) = 98.03%

c) we notice that as x increases from x=5 to x=60, the percentage of population that buys the game increases to a near 100% ; This makes sense in the context of the problem, since the greater is the advertisement of the problem, the higher is the commercial success in terms of customer converion form the population;

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