In 2010 the birthrate in a certain country increases from 11*(e^(0.04*t)) million births per year to 16*(e^(0.04*t)) million births per year, where t is the number of years since January 1, 2010.

Question

Set up the integral and find the projected increase in population that would result due to the higher birth rate between January 1, 2010 and January 1, 2029.

(Express the limits as exact numbers.)

Answer 1

Not sure what difference it makes what the rate was before 2010, since we are told that the rate after 2010 is 16e^(.04t) per year after 2010.

So, now we have

dp/dt = 16e^(.04t)
so, during the next 19 years, the population grows by
∫[0,19] 16e^(.04t) dt