Question

n 2000 the population of a small village was 2,400. With an annual growth rate of approximately 1.68%, compounded continuously, what will the population be in 2020 according to the exponential growth function? Round your answer to the nearest whole number, and do not include the units in your answer.

Answer 1

The population would be 3358

Explanation:

Since, exponential growth function if the growth is compound continuously,

`A = Pe^(rt)`

Where,

P = initial population,

r = growth rate per period,

t = number of periods,

Given,

The population in 2000, P = 2,400,

Growth rate per year = 1.68% = 0.0168,

Number of years from 2000 to 2020, t = 20,

Thus, the population in 2020,

`A=2400 e^(0.0168* 20)`

`=2400 e^(0.336)`

`= 3358.4136`

`\approx 3358`