a company begins a radio advertising campaign in a city to market a new cd - rom video game. the percentage…

a company begins a radio advertising campaign in a city to market a new cd - rom video game. the percentage of the target market that buys a game is given by the function, $f(t)=100(1 - e^{-0.02t})$, where $t$ is the number of days of the campaign and $f(t)$ is a percent. find the percentage of the target market that buys a game after a 30 - day campaign.\nwhat percentage of the target market is predicted to buy a game after a 30 - day campaign? $square%$ (round to the nearest hundredth.)

a company begins a radio advertising campaign in a city to market a new cd - rom video game. the percentage of the target market that buys a game is given by the function, $f(t)=100(1 - e^{-0.02t})$, where $t$ is the number of days of the campaign and $f(t)$ is a percent. find the percentage of the target market that buys a game after a 30 - day campaign.\nwhat percentage of the target market is predicted to buy a game after a 30 - day campaign? $square%$ (round to the nearest hundredth.)

Answer

Explanation:

Step1: Substitute t = 30 into the function

$f(30)=100(1 - e^{-0.02\times30})$

Step2: Calculate the exponent value

First, calculate $-0.02\times30=- 0.6$. Then $e^{-0.6}=\frac{1}{e^{0.6}}$. Using a calculator, $e^{0.6}\approx1.82212$, so $e^{-0.6}\approx\frac{1}{1.82212}\approx0.54881$.

Step3: Calculate the value of $1 - e^{-0.6}$

$1 - e^{-0.6}=1 - 0.54881 = 0.45119$.

Step4: Calculate the value of $f(30)$

$f(30)=100\times0.45119 = 45.119\approx45.12$.

Answer:

$45.12$