Exponential Functions

[john3j]

Can anyone help me figure out this problem or at least set up a formula so that I can solve it?

"the population of a certain city economically derpressed union is declining exponentially at a rate of 1.5 percent. if the population in 1990 was 30,000, estimate the population in 2010"

I am in a calculus class in college, fyi.

Thanks,
John

 

[soroban]

Hello, john3j!

This problem may have arisen in a Calculus class,
. . but it is not a Calculus problem.
It should have been explained much earlier.

The population of a certain region is declining exponentially at a rate of 1.5 percent.
If the population in 1990 was 30,000, estimate the population in 2010.

The population is decreasing at \(\displaystyle 1.5\% = 0.015\) per year.

Each year, the population is \(\displaystyle 98.5\% = 0.985\) of the previous year.


Let \(\displaystyle n\) = number of years since 1990.

The population function is: .\(\displaystyle P(n) \;=\;30,\!000(0.985)^n\)

Got it?