The population of a town was 14,000 in 2010. If the population decreased at a rate of 1.5% each year thereafter, use an exponential function to find the population after 10 years.
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Step-by-step explanation:
Answer: 120362
Step-by-step explanation:
The exponential function for finding population is given as :
A = P(1 + r)^{t}(1+r)
t
Where :
A = Total amount of growth after some given time
P = Original population
r = growth rate
t = total years
From the question , we will notice that there is a decrease in the population , then the formula to be used will be
A = P(1 - r)^{t}(1−r)
t
)
A = ?
P = 14000
r = 1.5% = 0.015
t = 10
substituting each given values into the formula , we have
A = 1400 ((1- 0.015)^{10}(1−0.015)
10
)
A = 14000 (0.985^{10}0.985
10
)
A = 14000 X 0.859730442
A = 120362.2619
Therefore : The population after 10 years is ≈ 120362
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