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.

$0.06\times 100=6\%$

Therefore, the rate of decrease is 6%.