The following function represents the value of a motorcycle, in dollars, after x years: f(x) = 19,000(0.91)x
what does 0.91 represent?
a. the present value of the motorcycle
b. the value of the motorcycle after x years
c. the decrease in the value of the motorcycle, which is 9%
d. the decrease in the value of the motorcycle, which is 91%

Option C.The decrease in the value of the motorcycle, which is 9%

Step-by-step explanation:

we have a exponential function of the form

where

a is the initial value

b represents growth or decay factor

If b >1 then it is an exponential growth

if 0<b<1 then it is an exponential decay

In this problem

a=$19,000

b=0.91 -----> it is exponential decay factor

Find the rate of decrease r

b=(1-r)

substitute

0.91=1-r

r=1-0.91=0.09

Convert to percentage

0.09*100=9%

therefore

0.91 represent the decrease in the value of the motorcycle, which is 9%

range =5

step-by-step explanation:

to find the range, we take the largest value and subtract the smallest value.

the largest value is 5

the smallest value is 0

the range is 5-0   =5