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. 9.9
B. 10.4
C. 10.7
D. 11.2

Answer 1

0.073

Explanation:

The question is about growth function and you are asked to find out the growth rate. Growth function has a format of

y = a(1+r)^t

Where

y= future value = S(t)

a= current value = 273

r= growth rate

t= time =t

Since its a growing function, the r will be positive. If its decay function then the r will be negative. As you can see, the growth rate value is located inside the parentheses. The growth rate of the function should be:

(1+r)= (1.073)

r= 1.073- 1

r= 0.073