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
ANSWERED 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