Question

In 2000, the population of a county was 25,300,987. The population decreased at a rate of 2% each year. What was the population in 2008?

Answer 1

Answer: In 2008 the population was 21,525,144

Step-by-step explanation:

You need to use the following formula for Exponential decay:

$P=P_0(1-r)^t$

Where $P_0$ is the initial population in the year 0, $r$ is the rate of decay and $t$ is the time.

In this case, you can identify that:

$P_0=25,300,987\\\\r=2\%\\\\t=8$

Therefore, substituting these values into the formula for Exponential decay, you get:

$P=P_0(1-r)^t\\\\P=(25,300,987)(1-\frac{2}{100})^8\\\\P=21,525,144$

Then, in 2008 the population was 21,525,144