Question

# In 2005, the population of a district was 28,300, With a continuous annual growth rate of approximately 7% what will the population be in 2020 according to the exponential growth function? Round the answer to the nearest whole number.

Exponential growth and decay
In 2005, the population of a district was 28,300, With a continuous annual growth rate of approximately 7% what will the population be in 2020 according to the exponential growth function? Round the answer to the nearest whole number.

2020-11-09

GIVEN DATA : The population in 2005 is 28,300.
Population is continuously increasing annually with the rate 7%
TO FIND : The population of district in 2020.
EXPONENTIAL GROWTH FUNCTION:
If a quantity grows continuously by a fixed percent, the pattern can be depicted by this function
$$A=A_oe^{rt}$$
where $$A_o$$ is the initial value.
A is amount after growth or decay
t is time period
e=2.7182
r is the growth or decay rate
From the given data In 2005 population is 28300 i.e at
$$t=0, A_o=28300$$
growth rate r=7%=0.07
we need to find the population in 2020 thud time period will be t=15
Use the data in the Continuous Exponential Growth function:
$$A=A_oe^{rt}$$
$$A=(28300)e^{((0.07)(1.5))}$$
$$A=(28300)e^{1.05}$$
$$A=(28300)(2.718)^{1.05}$$
A=(28300)(2.857)
A=80853
Thus the population in year 2020 is 80,853 people