Respuesta :
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:
[tex]P=1-e^{-0.047t}[/tex]
where [tex]t[/tex] 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 [tex]t=20[/tex] in the formula given.
We have:
[tex]P(t)=1-e^{-0.047t}[/tex]
Plugging in [tex]t=20[/tex]
[tex]P(20)=1-e^{-0.047(20)}[/tex]
[tex]P=1-e^{-0.94}[/tex]
[tex]P=1-e^{-0.047t}[/tex]
[tex]P=1-0.3906[/tex]
[tex]P=0.6094[/tex]
Thus, probability [tex]P[/tex] after 20 days = 0.6094
The probability in percentage can be given = [tex]0.6094\times 100[/tex]= 60.9%
