Question

In 2015, the population of a district was 10,600. With an annual growth rate of approximately 4%, what will the population be in 2040 according to the exponential growth function

Answer 1

`19,090\ people`

Explanation:

we know that

The equation of a exponential growth function is given by

`y=a(1+r)^x`

where

y is the population

x is the time in years since year 2015

a is the initial value

r is the rate of change

we have

`a=10,600\\r=4\%=4/100=0.04`

substitute

`y=10,600(1+0.04)^x`

`y=10,600(1.04)^x`

In the year 2040 the value of x is equal to

`x=2040-2015=25\ years`

substitute

`y=10,600(1.04)^(15) =19,090\ people`