Question

Scientists were studying a rare species of parrot they went to fourth in the year 2010 and found there were 608 pairs in the forest when the scientist went back five years later they found 4617 parents how many parents would expect her to be in 2016

Answer 1

6926 pairs in 2016.

Explanation:

The number of pairs in t years after 2010 is modeled by the following function:

`P(t) = P(0)(1+r)^(t)`

In which P(0) is the number of pairs in 2010 and r is the growth rate, as a decimal.

608 pairs in 2010

This means that
`P(0) = 608`

So

`P(t) = P(0)(1+r)^(t)`

`P(t) = 608(1+r)^(t)`

4617 pairs five year later.

So P(5) = 4617. We use this to find 1 + r.

`P(t) = 608(1+r)^(t)`

`4617 = 608(1+r)^(5)`

`(1+r)^(5) = (4617)/(608)`

`1 +r = \sqrt[5]{(4617)/(608)}`

`1 + r = 1.5`

So

`P(t) = 608(1.5)^(t)`

How many pairs in 2016?

2016 is 2016 - 2010 = 6 years after 2010. So this is P(6).

`P(t) = 608(1.5)^(t)`

`P(6) = 608(1.5)^(6) = 6926`

6926 pairs in 2016.