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'
[tex]114= ab^0[/tex] so a= 114
(36, 912)
[tex]912= 114b^{36}[/tex]
Divide both sides by 114 and then take 36th root on both sides
8 = b^36
b = 1.05946
so exponential equation is [tex]y= 114(1.05946)^x[/tex]
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
[tex]y= 114(1.05946)^{39}[/tex]
y= 1084.43336
so , 1084 rabbits after another 3 months
