Suppose that in any given year, the population of a certain endangered species is reduced by 25%. If the population is now 7500, in how many years will the population be 4000?(adsbygoogle = window.adsbygoogle || []).push({});

Well, I know that the formula for this is P(t) = Ce^{kt}.

I just can't figure out the value of k.

i did 7500 x .25 = 1875... 7500 - 1875 = 5625...

so i set up 7500x = 5625 and got .75.

so, essentially.. the population is growing at .75 per year.

so i used .75 as k and:

4000 = 7500e^(.75t)

4000/7500 = e^(.75t)

8/15 = e^(.75t)

ln(8/15) = .75t lne

ln(8/15) = .75t

t = [ln(8/15)] / .75

t = -.8381448792 years

This can't be correct because time isn't negative, and if you do it logically, it would be around 2. something years:

7500 x .75 = 5625 ----> 1 year

5625 x .75 = 4218.75 ----> 2 yrs

4218.75 x .75 = 3164.0625 ----> 3 yrs

So it's somewhere between 2 and 3 years... closer to 2 years.

and if i set up 4218.75x = 4000

x = .9481481481

so i know after 2 years.. i can multiply by .9481481481 and i get 4000..

but i don't know how to convert that into years.. since that is a percentage.

BLEH.. brain is about to explode.. don't know what to do.. lol

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# Homework Help: Exponential population decay word problem

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