Question

The Jackson school district purchases a high-volume copier for $15,400 After 10 years the copier will need to be replaced. It is estimated that the value of the copier depreciates by 18%What is the 1-year decay factor? What is the 1-year percent change? Let h be the function that defines the value of the copier after m years. What is the function h h(m)= Determine the value of the copier 8 years after it was purchased.Value after 8 years in dollars

Answer 1

decay factor = 0.82

percent change = 18%

Function: h(m) = 15400(0.82)^m

Value after 8 years = $3147.97

Step-by-step explanation:

If the copier depreciates by 18% each year, the decay factor will be:

d = 1 - r = 1 - 0.18 = 0.82

Because r is the rate of depreciation.

On the other hand, the percent change will be the rate of depreciation, so it is equal to 18%.

Finally, the function has the following form:

`h(m)=h_o\cdot d^m`

Where h0 is the initial value of the copier and d is the decay factor. So, the function for the value of the copier is:

h(m) = 15400(0.82)^m

Finally, the value of the copier 8 years after can be calculated replacing m by 8, so:

`\begin{gathered} h(m)=15400(0.82)^m \\ h(8)=15400(0.82)^8 \\ h(8)=15400(0.2044) \\ h(8)=3147.97 \end{gathered}`

So, the value after 8 years will be $3147.97

Therefore, the answers are:

decay factor = 0.82

percent change = 18%

Function: h(m) = 15400(0.82)^m

Value after 8 years = $3147.97