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Math Help - exponential decay

  1. #1
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    Post 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!
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  2. #2
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    Quote Originally Posted by live_laugh_luv27 View Post
    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
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  3. #3
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    and you got .75 by subtracting .25 from 1., right?
    Thanks for the help!
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