Suppose that in an election year, the proportion p of voters who recognize a certain candidate's name t months after the campaign started is given by . After how many months is the proportion maximized?
A)3 months
B)7 months
C)2 months
D)9 months
E)6 months

Question

Suppose that in an election year, the proportion p of voters who recognize a certain candidate's name t months after the campaign started is given by  . After how many months is the proportion maximized? ​
A)3 months 
B)7 months 
C)2 months 
D)9 months 
E)6 months

Quizplus · Accepted Answer

To find the value of t that maximizes the proportion p, we can take the derivative of p with respect to t and set it equal to zero. Differentiating p, we get:

p' = 11e^(t-5)/100 * (1/100)

Setting p' equal to zero and solving for t, we get:

11e^(t-5)/100 * (1/100) = 0
e^(t-5) = 0
t = 5

Since we started counting t at the beginning of the campaign, the value of t that maximizes p is 5 months after the campaign started, or 7 months into the campaign. Therefore, the answer is B) 7 months.

Suppose That in an Election Year, the Proportion P of Voters