Rate of Change - Help

Question

The population of a certain town was 10,000 in 1990. The rate of change of the population, measured in people per year, is modeled by , where t is measured in years since 1990. Discuss the meaning of . Calculate the change in population between 1995 and 2000. Do we have enough information to calculate the population in 2020? If so, what is the population in 2020? Explain your answers.

Answer 1

P(t) = P₀ + Integral from 0 to t of P'(t). You can think of the integral from 0 to 20 of P'(t) as the change in the population over 20 years from the original population in 1990 (i.e. the change in population from 1990 to 2010).

1995 to 2000. Integrate from t = 5 to 10

2020 is t = 30

P(30 = 10000 + integral from 0 to 30 of P'(t)

Indefinite integral of 200e^-.02t is( 200/(-.02))e^-.02t = -10000e^-.02t + c

Hope that helps.