Question

In 2000, the population of Snowy Egrets went from 5,000 individuals to 15,000 individuals. What is the growth rate over those 4 years?

Answer 1

`x=\sqrt[4]{3}-1` or
`x=0.316`

Explanation:

To write this equation you would need to use this equation for growth.

Final amount=initial amount (1+growth rate)^time

We have the final amount, 15,000, the initial amount, 5,000, and the time, 4 years. Now we have to plug in the values. We can write the growth rate as x.

`15,000=5000(1+x)^4`

Now start by dividing both sides by 5000.

`(15000)/(5000) =(1+x)^4`

`3=(1+x)^4`

Now you can find the fourth root of both sides to get rid of the exponent.

`\sqrt[4]{3} =1+x`

Finally, subtract 1 from both sides.

`x=\sqrt[4]{3}-1`

And, if allowed, you can use a calculator to find the value in decimal form which would be:

`x=0.316`