# A certain species of fish has been declining in population by 7% per year. That means its rate of decay is 0.93. What is the fish population in year 4 if the initial population was 500,000?

Jan 1, 2016

$374026$

#### Explanation:

This can be expressed as an exponential function in the form

$f \left(x\right) = a \left({b}^{x}\right)$,

where $a$ is the original amount, $b$ is the rate of decay, and $x$ is years elapsed. The function, when factoring in the information given in the question, is

$f \left(x\right) = 500000 \left({0.93}^{x}\right)$

$f \left(4\right)$ will give the population after four years have passed.

$f \left(4\right) = 500000 \left({0.93}^{4}\right) \approx 374026$