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

Answer:

$19,090\ people$

Step-by-step 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

$y=10,600(1.04)^{15} =19,090\ people$