Question

Can someone please help me with this exponential growth problem?
The population of a city increases in size by 18 percent every 10 years.

For each of the following, give your answer correct to two decimal places.

A) By what percentage will the population have increased after 21 years?

B) At what rate would the be population growing when there are thirteen hundred thousand people living in the city?

C) At what rate will the population be growing 2 years later?

Thanks!

Answer 1

N = N(0) exp (kt)

t=10
N/N(0) = exp(10 k)
ln(1.18) = 10 k
k = 0.0166 or 1.66% per year continuous growth

a) N/N(0) = exp(21 k) = 1.416 increase of 41.6 %

b) dN/dt = N(0) (k) exp(kt) =(300,000) k = 4980

c) for you to do now

Answer 2

You may want to do B) again after you figure out if the population is thirteen hundred thousand people (1,300,000) or three hundred thousand people (300,000) — @douglaswinslowcooper did the latter, but your problem statement has the former.