# exponential decay

• Aug 4th 2009, 04:47 PM
live_laugh_luv27
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!
• Aug 4th 2009, 05:18 PM
skeeter
Quote:

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!

$\displaystyle P = 7500(.75)^t$

$\displaystyle 4000 = 7500(.75)^t$

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

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

$\displaystyle t = \frac{\log\left(\frac{4000}{7500}\right)}{\log(.75 )} \approx 2.2$ years
• Aug 4th 2009, 05:23 PM
live_laugh_luv27
and you got .75 by subtracting .25 from 1., right?
Thanks for the help!