Question

Can someone please help me solve the problem

Answer 1

Given:

The exponential function is:

`y=630(0.94)^x`

To find:

The percentage rate of increase or decrease.

Solution:

The general exponential function is:

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

Where, a is the initial value, |r| is the growth rate in decimals if r>0 and |r| is the decay rate in decimal if r<0.

The exponential function is:

`y=630(0.94)^x`

It can be written as:

`y=630(1-0.06)^x`

`y=630(1+(-0.06))^x` ...(ii)

On comparing (i) and (ii), we get

`r=-0.06`

Since r is negative, therefore the given function is a decreasing or decay function.

Now,

`|r|=|-0.06|`

`|r|=0.06`

So, the rate of decrease is 0.06. Multiply this number by 100 to get the percentage.

`0.06* 100=6\%`

Therefore, the rate of decrease is 6%.