Question

Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. y=2600(0.3)^x y=2600(0.3) x

Answer 1

Explanation:

Answer 2

Decay function, 70% per year.

Explanation:

A general exponential function is defined as

`y=a(1+r)^x` ...(1)

where, a is initial value, |r| is rate of change and x is time in years.

If r>0, then it is a growth function and if r<0, then it is a decay function.

The given function is

`y=2600(0.3)^x`

It can be rewritten as

`y=2600(1-0.7)^x`

`y=2600(1+(-0.7))^x` ...(2)

On comparing (1) and (2), we get

`r=-0.7`

Since r<0, therefore the given function is a decay function.

`|r|=|-0.7|=0.7=70\%`

Therefore, the given function decreasing by 70% per year.