Answer:
[tex]P(t) = 608(1.5)^{t}[/tex]
Step-by-step explanation:
The number of parrots in t years after 2010 can be modeled by the following function:
[tex]P(t) = P(0)(1+r)^{t}[/tex]
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 [tex]P(0) = 608[/tex]
Then
[tex]P(t) = 608(1+r)^{t}[/tex]
When the scientists went back 5 years later, they found 4617 parrots.
This means that [tex]P(5) = 4617[/tex]
We use this to find 1 + r. So
[tex]P(t) = 608(1+r)^{t}[/tex]
[tex]4617 = 608(1+r)^{5}[/tex]
[tex](1+r)^{5} = \frac{4617}{608}[/tex]
[tex]1 + r = \sqrt[5]{\frac{4617}{608}}[/tex]
[tex]1 + r = 1.5[/tex]
So
[tex]P(t) = 608(1.5)^{t}[/tex]
