Question

f(x)=275550(0.89)^x represents the value of a motor home x years since 2005. what is the average rate of change of the value of the motor home from 2010 to 2013?

Answer 1

If
`f(x)=275550(0.89)^x` represents the value of a motor home x years since 2005, the average rate of change of the value of the motor home from 2010 to 2013 is 11%.

The average rate of change represents the constant ratio or rate of decrease occurring in the value of the motor home since 2005.

From the exponential decay function,
`f(x)=275550(0.89)^x`, we can equate the following values:

275550 is the initial value of the motor home.

x refers to the time interval.

0.89 represents the decay factor.

f(x) is the final value.

The decay factor is determined as (1 - r), where r is the rate of change.

0.89 = 1 - r

r = 0.11 (1 - 0.89)

r = 11% (0.11 x 100)

Thus, the average rate of change is 11%.