Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and the Yahoo Answers website is now in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.

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

  • 1 decade ago
    Favorite 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.

Still have questions? Get your answers by asking now.