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?a. f(x) = 3460(1.35)x where 1.35 is the rate of growth.b. f(x) = (3460 ⋅ 1.35)x where 1.35 is the rate of growth.c. f(x) = 1.35(3460)x where 3460 is the rate of growth.d. f(x) = 3460(x)1.35 where 3460 is the rate of growth.

Answer 1

The function is
`f(x)=3460(1.35)^x` where 1.35 is the rate of growth.

Explanation:

We know that the population was 3,460 last year and has been increasing by 1.35 times each year.

This is an example of an Exponential Growth:

Exponential growth happens when an initial population increases by the same percentage or factor over equal time increments or generations.

So we have a generally useful formula:

`y(x)=a\cdot b^x`

where

a = Initial value

b = Rate of growth

We know the initial value a = 3,460 and b = 1.35. Therefore the function to model is
`f(x)=3460(1.35)^x` where 1.35 is the rate of growth.