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The size P of a small herbivore population at time t (in years) obeys the function P(t) = 1000e0-16t if they have enough food and the predator population stays constant. After how many years will the population reach 4000?

User Budhajeewa
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Answer:

After 9 years, the population reach 4000.

Explanation:

The given function P(t) represents the size of a small herbivore population at time t (in years).


P(t)=1000e^(0.16t)

We need to find the number of years after which population reach 4000.

Substitute P(t)=4000 in the above function.


4000=1000e^(0.16t)

Divide both sides by 1000.


4=e^(0.16t)

Taking ln on both sides.


\ln 4=\ln e^(0.16t)


1.3863=0.16t
[\because \ln e^x=x]

Divide both sides by 0.16.


(1.3863)/(0.16)=t


8.664375=t

We need to find the number of years. So, round the answer to the next whole number.


t\approx 9

Therefore, after 9 years, the population reach 4000.

User Harry Lime
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