 # 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. Nannie Mack 2020-11-08 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.
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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
$A={A}_{o}{e}^{rt}$
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:
$A={A}_{o}{e}^{rt}$
$A=\left(28300\right){e}^{\left(\left(0.07\right)\left(1.5\right)\right)}$
$A=\left(28300\right){e}^{1.05}$
$A=\left(28300\right)\left(2.718{\right)}^{1.05}$
A=(28300)(2.857)
A=80853
Thus the population in year 2020 is 80,853 people