Question

suppose that a company introduces a new computer game in a city using television advertisements. surveys show that p% of the target audience buy the game after x ads are broadcast, satisfying the equation below. complete parts (a) through (d)
p(x)=\frac{100}{1 + 51e^{-0.14x}}
a) what percentage buy the game without seeing a tv ad (x = 0)?
% (type an integer or a decimal rounded to the nearest tenth as needed.)

Explanation:

Step1: Substitute x = 0 into the function

Substitute \(x = 0\) into \(P(x)=\frac{100}{1 + 51e^{-0.14x}}\). Since \(e^{-0.14\times0}=e^{0}=1\), the function becomes \(P(0)=\frac{100}{1 + 51\times1}\).

Step2: Calculate the value of P(0)

First, calculate the denominator \(1+51\times1=1 + 51=52\). Then, \(P(0)=\frac{100}{52}\approx1.9\).

Answer:

1.9