Question

The bear population in a certain region has been declining at a continuous rate of

2% per year. In 2012 there were 965 bears counted in the area.

a) Write a function f(t) that models the number of bears t years after 2012.

b) What is the population of bears predicted to be in 2020?

Answer 1

Explanation:

a) The function f(t) that models the number of bears t years after 2012 can be expressed using exponential decay, as follows:

f(t) = 965 * (0.98)^(t)

Where 0.98 represents the rate of decline of 2% per year. The starting point for t is 0, which corresponds to the year 2012.

b) To find the population of bears predicted to be in 2020, we need to evaluate f(8) since 2020 is 8 years after 2012:

f(8) = 965 * (0.98)^(8)

= 834.84 (rounded to two decimal places)

Therefore, the predicted population of bears in 2020 is approximately 835.