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

c. 60.9%

Explanation:

Answer 2

c. 60.9%

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* 100`= 60.9%