Question

Derek found a function that approximately models the population of iguanas in a reptile garden, where x represents the number of year since the iguanas were introduced into the garden

i(x) = 12(1.9)^x

Rewrite this function in a form that reveals the monthly grow rate of the population of iguanas in the garden. Round the growth factor to the nearest thousandth

Answer 1

the answer is i(x)12x(1+0.9/12)^12x

Answer 2

Monthly growth function is
`i(x)=12 * (1+(0.9)/(12))^(12x)` and growth rate is 0.075.

Explanation:

We are given,

The function which models the population of iguanas in a reptile garden is
`i(x)=12 * 1.9^(x)`, where x is the number of years.

As,
`i(x)=12 * 1.9^(x)`

i.e.
`i(x)=12 * (1+0.9)^(x)`

So, the monthly growth rate function becomes,

`i(x)=12 * (1+(0.9)/(12))^(x * 12)`

i.e.
`i(x)=12 * (1+(0.9)/(12))^(12x)`.

Hence, the monthly growth rate population of iguanas is i.e.
`i(x)=12 * (1+(0.9)/(12))^(12x)`.

Moreover, the growth factor is
`(0.9)/(12)` = 0.075.

Hence, the growth factor rounded to nearest thousandth is 0.075