The number of ants in a colony at time t (in days) is modeled by . What is the one-week growth factor for the number of ants (rounded to the nearest hundredth)?

Question

The number of ants in a colony at time t (in days) is modeled by  . What is the one-week growth factor for the number of ants (rounded to the nearest hundredth)?

Quizplus · Accepted Answer

To find the one-week growth factor, we need to evaluate the expression at t=7 (since 1 week = 7 days).

11e^(0.3(7)) = 11e^(2.1) ≈ 47.68

So the one-week growth factor is approximately 47.68/11 ≈ 4.77.

Therefore, the best choice is B.

The Number of Ants in a Colony at Time T