Question

no calculator is allowed on this question.
the population of rabbits in a certain forest can be modeled using a sinusoidal function of time. a minimum population of 500 rabbits occurs at month 3. the next maximum population of 540 rabbits occurs at month 9. what is the period of the sinusoidal model?
select one answer
a 6 months
b 9 months
c 12 months
d 20 rabbits

Explanation:

Step1: Understand sinusoidal period relation

In a sinusoidal function, the distance between a minimum and the next maximum is half of the period. Let the period be \( T \). The time between minimum (month 3) and next maximum (month 9) is \( 9 - 3 = 6 \) months. This 6 months is \( \frac{T}{2} \).

Step2: Calculate the period

Since \( \frac{T}{2}=6 \), multiply both sides by 2: \( T = 6\times2 = 12 \) months.

Answer:

C. 12 months