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 maximum proportion of voters who recognize the candidate's name, we need to find the maximum value of p(t). To do this, we take the derivative of p(t) with respect to t and set it equal to zero:

p'(t) = (11/80)te^(-t/8) = 0

Solving for t, we get t = 0 or t = 8. Since t = 0 doesn't make sense in this context (the campaign hasn't started yet), we choose t = 8. Therefore, the proportion is maximized after 8 months or 7 months after the start of the campaign.

Thus, the answer is B) 7 months.

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