Question

A study of the annual population of gray squirrels in a Texas state park shows the population, S(t), can be represented by the function S(t) = 273(1.073)t , where the t represents the number of years since the study started. Based on the function, what is the growth rate? A) 1 B) 0.073 C) 1.073 D) 273

Answer 1

The growth rate of the given function is A) 1

Explanation:

Step 1; To calculate the rate we need to see the difference between values at different periods of time. We need to calculate the population at different times.

For t = 1 years, S(t) = 273(1.073)t = 273 × 1.073 × 1 = 292.929,

For t = 2 years, S(t) = 273(1.073)t = 273 × 1.073 × 2 = 585.858,

For t = 2 years, S(t) = 273(1.073)t = 273 × 1.073 × 1 = 878.787.

Step 2; To calculate the growth rate, we divide the difference in the values of the present year and the past year by the value in the past year.

Growth rate between t = 1 and t = 2, Growth rate = S(t=2) - S(t=1) / S(t=1)

= 585.858 - 292.929 / 292.929 = 1.

Growth rate between t = 2 and t = 3, Growth rate = S(t=3) - S(t=2) / S(t=2)

= 878.787 - 585.858 / 585.858 = 1.

So the growth rate is A) 1.