Question

Wes has been tracking the population of a town. The population was 3,460 last year and has been increasing by 1.35 times each year. How can Wes develop a function to model this?

Answer 1

After x years the population of a town is 3460*[(1.35)^x]

Answer 2

`y=3460(1.35)^x`, where, 1.35 is the rate of growth.

Explanation:

Let x be the number of years and y be the population.

We have been given that Wes has been tracking the population of a town. The population was 3,460 last year and has been increasing by 1.35 times each year.

Since the population increases exponentially, so we can use an exponential function to model the growth of population.

An exponential function is in form
`y=a*b^x`, where,

a = Initial value,

b = Rate of growth,

As our given growth rate is 1.35 and initial population was 3,460, so upon substituting these values in exponential growth formula we will get,

`y=3460(1.35)^x`, where, 1.35 is the rate of growth.

Therefore, the function
`y=3460(1.35)^x` models our given situation.