Problem

Suppose that a company introduces a new computer game in a city using television advertisements. Surveys show that $\mathrm{P} \%$ of the target audience buy the game after $x$ ads are broadcast, satisfying the equation below. Complete parts (a) through (d). \[ P(x)=\frac{100}{1+51 e^{-0.1 x}} \] a) What percentage buy the game without seeing a TV ad $(\mathrm{x}=0)$ ? $\%$ (Type an integer or a decimal rounded to the nearest tenth as needed.)

Solution

Step 1 :The question is asking for the percentage of the target audience that buys the game without seeing a TV ad. This corresponds to the value of P when x=0. We can substitute x=0 into the equation to find this value.

Step 2 :Substitute x=0 into the equation: \(P(x)=\frac{100}{1+51 e^{-0.1 x}}\)

Step 3 :After substituting, we get: \(P = 1.9230769230769231\)

Step 4 :Final Answer: The percentage of the target audience that buys the game without seeing a TV ad is approximately \(\boxed{1.9\%}\).

From Solvely APP
Source: https://solvelyapp.com/problems/35798/

Get free Solvely APP to solve your own problems!

solvely Solvely
Download