# Math Help - exponential decay

1. ## exponential decay

Each year, the population of endangered birds is reduced by 25%. If the current population is now 7500, in how many years will the population be 4000?

I got the answer 1.58 years...is this correct? What is the correct formula to use for this problem?

Thanks!

2. Originally Posted by live_laugh_luv27
Each year, the population of endangered birds is reduced by 25%. If the current population is now 7500, in how many years will the population be 4000?

I got the answer 1.58 years...is this correct? What is the correct formula to use for this problem?

Thanks!
$P = 7500(.75)^t$

$4000 = 7500(.75)^t$

$\frac{4000}{7500} = (.75)^t$

$\log\left(\frac{4000}{7500}\right) = t \log(.75)$

$t = \frac{\log\left(\frac{4000}{7500}\right)}{\log(.75 )} \approx 2.2$ years

3. and you got .75 by subtracting .25 from 1., right?
Thanks for the help!