SOLUTION: Hi. I'm not sure how to solve this problem. I'm assuming it has to do with derivatives. Thank you. On a certain island there are two populations of deer. After t years the numbe

Question 721098: Hi. I'm not sure how to solve this problem. I'm assuming it has to do with derivatives. Thank you.
On a certain island there are two populations of deer. After t years the numbers of deer in the two populations are p(t) = 100 e^t and q(t) = 1000 e^-t. When is the total population smallest?
t=________
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The total population is
The derivative of that function would be the population growth rate

When that growth is zero the population will have reached its minimum:

If we define then and we can solve
as a first step
--> --> --> --> -->
In terms of
--> --> --> or = approx
So the total deer population will reach its minimum after about 1.151 years.
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