Question

9. The population of a town is 2500 and is decreasing at a rate of 3.5% per year. Write an exponential function to find the population of the town after 5 years. y = (a) ([6] + [e]) Please enter the appropriate values for a, b,cand d. The population after 5 years would be Round your answer to the nearest whole number (you can not have part of a living being).

Answer 1

The original population is 2500

The decreasing rate is 3.5%/year

You have to write the expression for the exponential decay and calculate the population of the town after 5 years.

An exponential decay can be calculated as:

$y=a(1-r)^x$

Where

a is the initial value

r is the decay rate → expressed as a decimal value

x is the time that have passed

Express that rate as a decimal value:

r=3.5/100=0.035

The exponential decay for this population can be expressed as:

$y=2500(1-0.035)^x$

For x=5 years the population (y) will be:

$\begin{gathered} y=2500(1-0.035)^5 \\ y=2092.07\cong2093 \end{gathered}$

After 5 years the population will be 2093