Question

The population of a small town was 4,000 in 2016 and it is 4,050 in 2018. Use the Malthusian model in order to predict the population of the same town in 2020. Do not simplify your answer.

Answer 1

Explanation:

As per Malthusian population theory

`{ P(t)=P_(0)e^(rt)}` where P0 = initial population in 2016 = 4000

and t = no of years from 2016

We are given P(2) =4050

i.e.
`4000e^rt} =4050\\2r=log (4050)/(4000) =0.0124\\r=0.0062`

Hence we have

`P(t)=4000e^(0.0062t)`

Using this in 2020, t = 4.

Population in 2020 =
`P(4)=4000e^(0.0062*4)\\=4100.43\\`