Really need lots of help on how to do this Math problem,

[chilledsoup]

Suppose a dump truck purchased new for $150,000 by the ABC construction company has an expected useful life of 10 years and has an expected salvage value of $30,000 at the end of that time. IRS allows the loss in value of the truck as a deductible expense of doing 'business. Although there are a number of methods for determining the annual amount of depreciation, the simplest is the straight-line method. Using this model, the company assumes that the value V, at any time, t, can be represented by a straight line that contains the two ordered pairs, (0, 150,000) and (10,30,000).

a. Describe how to interpret the two ordered pairs.
b. Determine the equation of the line that passes through the two ordered pairs and draw the graph.
c. Interpret the slope within the context of the problem. What does the y-intercept stand for?
d. What are the domain and range of the linear function in (b)? How does this differ trom the domain and range within context of problem?

 

[soroban]

Hello, chilledsoup!

This is just a straight-line problem . . . Exactly where is your difficulty?

The problem itself has poor wording.
. . It names variables V and t, and asks for: V = f(t).
. . But later, it refers to the y-intercept. (?)
I'll change the wording . . .

Suppose a dump truck purchased new for $150,000 by the ABC
construction company has an expected useful life of 10 years
and has an expected salvage value of $30,000 at the end of that time.
IRS allows the loss in value of the truck as a deductible expense of 'doing business'.
Although there are a number of methods for determining the annual amount of depreciation,
the simplest is the straight-line method.
Using this model, the company assumes that the value y, at any time x can be represented
by a straight line that contains the two ordered pairs, (0, 150,000) and (10,30,000).

a. Describe how to interpret the two ordered pairs.

The first pair (0, 150,000) means: at time 0, the Value is $150,000.
The second pair (10, 30,000) means: after 10 years, the value is $30,000.

b. Determine the equation of the line that passes through the two ordered pairs and draw the graph.

You're expected to be able to write the equation of a line, given two points.

. . . . . . . . . . . . y₂ - y₁ . . . 30,000 - 150,000 . . . . -120,000
Slope: . m . = . -------- . = . ---------------------- . = . ----------- . = . -12,000
. . . . . . . . . . . . x₂ - x₁ . . . . . . . .10 - 0 . . . . . . . . . . . 10


We have the slope, m = -12,000, and the y-intercept, b = 150,000

. . . y .= .-12,000x + 150,000

c. Interpret the slope within the context of the problem.
What does the y-intercept stand for?

The slope, m = -12,000, means that the truck loses $12,000 of its value each year.

The y-intercept, b = 150,000, is the original value of the truck (at t = 0).

d. What are the domain and range of the linear function in (b)?
How does this differ trom the domain and range within context of problem?

For a linear (straight line) function, the domain is the set of all real numbers: (-oo, oo)
. . and the range is the set of all real numbers: (-oo, oo)

In the problem, the domain is [0, 10] . . . and the range is [30,000, 150,000].

 

[chilledsoup]

how would you do the graph for b.

 

[chilledsoup]

i need to do a graph

 

[Gene]

Decide on a scale, put dots at the two ordered pairs and draw a line through them.