Question

A population of a certain species of turtle is 28,000 animals and is increasing at the rate of 2% per year.

This paragraph describes a(n) Select an answer linear growth linear decay exponential growth exponential decay  scenario.

Write an equation for y, the population at time t (in years), representing the situation.
y =     

How many turtles are in the population after 15 years?

Answer 1

The initial population is 28,000 and the growth rate is 2% per year.

At the end of first year the population is

2 2 2800028000 x 100 28000(1 100

At the end of second year population is increased by 2 % of the population in first year whic is

2 2 2 -) = 28000 (1+100 28000(1 -)(1 100 100

and so on..

The population after t years is

2 28000(1 100

Which is an exponential function and

So this is an exponential growth.

2 1 1 + 100

Let y = the population after t years. Then

2 y28000(1 100

For t = 15 we have

2 y28000(1 100 15 1.345868 37684.304 28000 x _

But y must be an integer. Hence the population after 15 years is 37684.