Question

In an effort to control vegetation overgrowth, 114 rabbits are released in an isolated area free of predators. After 3 years, it is estimated that the rabbit population has increased to 912. Assuming exponential population growth, what will the population be after another 3 months? Round to the nearest rabbit.

Answer 1

114 rabbits are released in an isolated area free of predators

When month =0 , the rabbits = 114

3 years = 36 months

When months = 36 , then rabbits = 912

(0,144) and (36, 912)

Exponential growth equation is y = ab^x

Plug in each point and solve for 'a'  and 'b'

$114= ab^0$  so a= 114

(36, 912)

$912= 114b^{36}$

Divide both sides by 114 and then take 36th root on both sides

8 = b^36

b = 1.05946

so exponential equation is $y= 114(1.05946)^x$

x is the number of months and y is the population

to find the population be after another 3 months

Plug in 36+3= 39 for x  and find out y

$y= 114(1.05946)^{39}$

y= 1084.43336

so , 1084 rabbits after another 3 months