Question

In 2005 the population of a district was 35.700 with a continuous annual growth rate of approximately 4%, what will the population be in 2030 according to the exponential growth function? Round the answer to the nearest whole numberdo not include the unit in your answer.

Answer 1

Given:

Population is 2005 = 35,700

growth rate = 4% = 0.04

To find:

The population in 2030.

Solution:

The general exponential growth model is

$y=a(1+r)^t$

where, a is initial value, r is growth rate and t is time in years.

Let the initial year is 2005. So, number of years between 2005 to 2030 is

$2030-2005=25$

Putting a=35,700, r=0.04 and t=25 in the above model.

$y=35,700(1+0.04)^{25}$

$y=35,700(1.04)^{25}$

$y=35,700(2.665836)$

$y=95170.3452$

Approximate the value to the nearest whole number.

$y\approx 95,170$

Therefore, population of the district will be about 95,170.