# How do you write an exponential function to model the situation. Then estimate the value of the function after 5 years. A population of 290 animals that increases at an annual rate of 9%?

Jul 8, 2018

$N = 290 \times {1.09}^{Y}$

#### Explanation:

An compounded increase of 9% means the growth factor is $1.09$, in other words the population will be multiplied by $1.09$ every year:

After 5 years the number will be:

$290 \times {1.09}^{5} = 290 \times 1 , 5386. . . \approx 446$

Note:
The general function is $N = B \times {G}^{T}$

Where $N =$ new, $B =$begin, $G =$growth factor, $T =$number of periods.

The growth factor can be derived from the percentage growth by:
$G = 1 \pm \frac{P}{100}$ where $P =$percentage growth (or decline).