Question

Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. y=8800(0.93)^x

Answer 1

y= 16(0.25)^x

The exponential equation represents an exponential decay because the rate of decay is 0.25 which is less than 1.

The general form equation is:

y(x)= a(1-r)^x such that r is the decay percent.

Comparing two equation we have 1-r = 0.25

==> r= 1-0.25 = 0.75 = 75%

 

2. y= 0.8(1.8)^x

The equation represents exponential growth because the growth factor is greater than 1.

==> 1+r = 1.8

==> r= 0.8 = 80%

Then, the growth percent is 80%

 

3. y= 17(1/5)^x

The equation represents exponential decay because 1/5 is less than 1.

==> 1-r = 1/5

==> r= 1- 1/5 = 4/5 = 0.8= 80%