https://file.aiquickdraw.com/mathbot/file/17289856762299qy6zdbu.jpg

The problem in the image involves a linear depreciation function for a copier machine, where the function $ V(t) = -3500t + 20000 $ gives the value $ V $ of the copier after $ t $ years.

Let's break down the solution for each part:

### a. Value of the copier after 3 years and 6 months:
Here, $ t = 3.5 $ years.

Substitute $ t = 3.5 $ into the equation:
\[
V(3.5) = -3500(3.5) + 20000
\]
\[
V(3.5) = -12250 + 20000 = 7750
\]

So, after 3 years and 6 months, the copier is worth **$7,750**.

### b. Salvage value of the copier after 5 years:
Here, $ t = 5 $.

Substitute $ t = 5 $ into the equation:
\[
V(5) = -3500(5) + 20000
\]
\[
V(5) = -17500 + 20000 = 2500
\]

So, after 5 years, the salvage value of the copier is **$2,500**.

### c. Domain of the function:
The copier depreciates over 5 years, so $ t $ is between 0 and 5 years.

Thus, the domain is:
\[
0 \leq t \leq 5
\]

### d. Sketch the graph:
This is a straight line graph since the function is linear. The two key points are:
- At $ t = 0 $, $ V(0) = 20000 $.
- At $ t = 5 $, $ V(5) = 2500 $.

Plot these two points and draw a straight line through them to get the graph of the depreciation function.

---

Would you like further details or explanations on any part? Here are 5 related questions to deepen your understanding:

1. How do you calculate the value of the copier after any arbitrary time $ t $?
2. What happens to the value of the copier beyond 5 years?
3. What does the slope of the depreciation function represent in this context?
4. How could you find the time when the copier's value becomes zero using the given function?
5. What is the significance of the y-intercept in the depreciation function?

**Tip:** Always check the units of your variables (years, dollars) to ensure you're interpreting the function correctly when substituting values.

The function V(t) = -3500t + 20000, where V is value and t is time in years, can be used to find the value of a large copy machine during the first 5 years of use. a) What is the value of the copier after 3 years and 6 months? b) What is the salvage value of the copier if it is replaced after 5 years? c) State the domain of this function. d) Sketch the graph of this function.

Solve a linear depreciation problem where a copier's value decreases over 5 years with the function V(t) = -3500t + 20000. Includes steps to find value after 3 years and 6 months, salvage value after 5 years, domain of the function, and graphing the result. Suitable for high school students in grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation