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

Answer:

Decay function, 70% per year.

Step-by-step 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.