Question

The bear population in RI has been increasing by 8% each year. In the year 2010 there were only 20 bears spotted in RI. Based on this info,

a. create a function a(t) that represents the bear pop, t years since 2010
b. determine bear pop in 2020
c. find out when there are more than 100 bears​

Answer 1

See below in bold.

Explanation:

a. The factor of growth = 1.08 per year so

P = 20(1.08)^t where P = the bear population and t = the time in years since 2010.

b. It is 10 years after 2010 so:

In 2020: P = 20 * (1.08)^10

= 43 bears.

c. When P = 100 we have:

100 = 20 * (1.08)^t

(1.08)^t = 100/20 = 5

t ln 1.08 = ln 5

t = 20.9 years.

So there will be more than 100 bears in the year 2010 + 21

= 2031.