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# If a population grows........?

If a population grows at a rate of r(t) people per year, what does

∫ r'(t) from t=0 to 10 represent?

Answer: It represents the total amount of people born during 10 years

Why is this the answer?

### 1 Answer

- Alfredo KrausLv 71 decade agoFavorite Answer
It is not. If the population at time t is p(t) then the rate of growth is dp/dt = r(t) and therefore the increase in population during 10 years is ∫ r(t) dt from t=0 to 10. Notice two things. First, it is the net increase in population, not the number of people born. The net increase accounts for things like people moving in or out and people dying as well as people being born.

Secondly, it is the integral of r(t) not r ' (t). The integral ∫ r'(t) dt from t=0 to 10 is just r(10)-r(0) and that is the increase in the rate of growth in the interval of 10 years.

I hope this helped.