(Can someone show me step by step?)The population of a small town is increasing at a continuous growth rate of 3.29 % per year. In 2018 the population was 15,000.

Question

Part A: If t is the number of years since 2018 and f(t) is the population, write a continuous exponential growth function expressing the relationship between f(t) and t.

PART B: Predict the year that the population will double in size.

Answer 1

3.29 % = 3.29 / 100 = 0.0329

So every year we multiply the population by 1 + 0.0329 = 1.0329

So 2019 pop = 15000 x 1.0329

In 2020 it is 15000 x 1.0329 x 1.0329

etc

So t years after 2018, it is 15000 x 1.0329^t

f(t) = 15000 x 1.0329^t

Population doubles when 1.0329^t = 2

t ln 1.0329 = ln 2

t = ln 2 / ln 1.0329 = 21.4

So population will double during the year 2018 + 21 = 2039