Question

Scientists were studying a rare species of parrot. They went to a forest in the year

2010 and found there were 608 parrots in the forest. When the scientists went back

5 years later, they found 4617 parrots. Which is the function to show p, the number

of parrots t years after 2010.

Answer 1

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

Explanation:

The number of parrots in t years after 2010 can be modeled by the following function:

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

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

608 parrots in the forest in 2010.

This means that
`P(0) = 608`

Then

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

When the scientists went back 5 years later, they found 4617 parrots.

This means that
`P(5) = 4617`

We use this to find 1 + r. So

`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)`