Question

The probability, P, that a person responds to an advertisement can be modeled by the exponential function P = 1 – e^-0.047t. In the formula, t is the number of days since the advertisement first appeared. What is the probability that a person has responded after 20 days?
a.20.9%
b.45.3%
c.60.9%
d.98.5%

Answer 1

Answer:

c. 60.9%

Step-by-step explanation:

Given:

The probability P that a person responds to an advertisement can be modeled by the function:

$P=1-e^{-0.047t}$

where $t$ represents number of days since the advertisement first appeared.

To find the probability that a person has responded after 20 days.

Solution:

In order to find the probability that a person has responded after 20 days, we will plugin $t=20$ in the formula given.

We have:

$P(t)=1-e^{-0.047t}$

Plugging in $t=20$

$P(20)=1-e^{-0.047(20)}$

$P=1-e^{-0.94}$

$P=1-e^{-0.047t}$

$P=1-0.3906$

$P=0.6094$

Thus, probability $P$ after 20 days = 0.6094

The probability in percentage can be given = $0.6094\times 100$= 60.9%