Q13. - Algebra 2

Question

In a certain wildlife refuge, the population of field mice can be modelled by $y=3000+1250\sin \left(\frac{\pi t}{6}\right)$, where (y) represents the number of mice and (t) represents the number of months past March 1 of a given year then determine the period of the function. What does this period represent?

Step-by-Step Solution

Answer

The period of the function is $12$ months and it represents that after every $12$ months past March 1 of the given year the given function repeats itself.

Step 1. Write down the given information.

The population of field mice is modelled by the equation $y=3000+1250\sin \left(\frac{\pi t}{6}\right)$, where (y) represents the number of mice and (t) represents the number of months past March 1 of the given year.

Step 2. Calculation.

From the given equation $y=3000+1250\sin \left(\frac{\pi t}{6}\right)$, the period $\left(P\right)$ of the function is evaluated as:

 $\begin{array}{c}P=\frac{2\pi }{\frac{\pi }{6}}\\ =12\end{array}$

Hence, the period of the function is 12 months and it represents that after every 12 months past March 1 of the given year the given function repeats itself.

Step 3. Conclusion.

The period of the function is $12$ months and it represents that after every $12$ months past March 1 of the given year the given function repeats itself.