The mouse population in a small desert area is modeled by the function where is measured in days. When is the maximum population attained and what is the maximum population?
A) After 175 days the mouse population is 0.
B) After 9 days the mouse population is 1310.
C) After 84 days the mouse population is 1310.
D) After 84 days the mouse population is 7005.
E) After 9 days the mouse population is 2485.

Question

The mouse population in a small desert area is modeled by the function  where  is measured in days. When is the maximum population attained and what is the maximum population?
A) After 175 days the mouse population is 0. 
B) After 9 days the mouse population is 1310. 
C) After 84 days the mouse population is 1310. 
D) After 84 days the mouse population is 7005. 
E) After 9 days the mouse population is 2485.

Quizplus · Accepted Answer

To find the maximum population, we need to find the maximum value of the given function. Taking the derivative of the given function, we get:

f'(t) = 120t^2 - 2600t + 11000

Setting this derivative equal to zero to find critical points:

120t^2 - 2600t + 11000 = 0

Dividing both sides by 20 gives:

6t^2 - 130t + 550 = 0

Solving using the quadratic formula, we get:

t = 5/3 or t = 25/3

We can discard t = 5/3 since we need the maximum value and not the minimum value. So, the maximum population is attained at t = 25/3 days.

Plugging this value back into the original function, we get:

f(25/3) = 7005.56

Therefore, the maximum population is 7005 and the correct answer is D.

The Mouse Population in a Small Desert Area Is Modeled