Question

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

Answer 1

Answer:

$P(t) = 608(1.5)^{t}$

Step-by-step 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

$P(t) = 608(1+r)^{t}$

$4617 = 608(1+r)^{5}$

$(1+r)^{5} = \frac{4617}{608}$

$1 + r = \sqrt[5]{\frac{4617}{608}}$

$1 + r = 1.5$

So

$P(t) = 608(1.5)^{t}$