Question

The population of a town is 75 000 and decreases 15% each year. Complete the exponential function that models the population afterx years

f(x) = 75,000

Answer 1

Explanation:

This is an exponential function of the form:

`y=a(1-r)^x` where a is the initial value and (1 - r) is the growth rate (which in our case is a decay, actually!). Our initial value is 75000 and our rate of change in the population is 15% or .15. Filling in our model:

`y=75000(1-.15)^x` and simplifying:

`y=75000(.85)^x` This turns out to be a decay problem because the value inside the parenthesis is less than 100%.

x is our time, so the model is as stated above.