A) Express the value of the bulldozer, V, as a function of how many years old it is, t. Make sure to use function notation

Question

Depreciation is the decrease or loss in value of an item due to age, wear, or market conditions. We usually consider depreciation on expensive items like cars. Businesses use depreciation as a loss when calculating their income and taxes.

One company buys a new bulldozer for $124950. The company depreciates the bulldozer linearly over its useful life of 19 years. Its salvage value at the end of 19 years is $11900.

A) Express the value of the bulldozer, V, as a function of how many years old it is, t. Make sure to use function notation.

B) The value of the bulldozer after 6 years is $

Answer 1

A.

One important piece of information is that the bulldozer depreciation is "linear". This means a "straight line" if graphed (the "line" in "linear"). This means the depreciation can be represented by one of the 3 forms of linear equations:

y=mx+b, slope intercept

y-y=m(x-x), point slope, rewritten as y=m(x-x)+y to set up to convert to function notation.

Ax+By=C, standard form, rewritten as y=(C-Ax)/B to set up to convert to function notation.

m signifies the slope, which is the same as the rate of change, or the change in y divided by the change in x. In our problem, V is expressed as a function of t, so –

m=($124950–$11900)/(0years–19years)= –$5950

Keeping in mind the the changes have to be calculated in the same direction, i.e.

the result of starting value minus end value divided by the result of the start time minus the end time OR

the result of end value minus start value divided by the result of the end time minus the start time.

In the slope intercept form of linear equation, b is the y intercept, or the value of y when x is zero.

We are given that when time starts (upon purchase), t=0, the value of the bulldozer, V, is $124950.

So, by using y=mx+b, we have

V(t)= –($5950years)t+$124950

B.

V(6)= –($5950years)(6)+.$124950

You can make the final calculation.

Answer 2

(124950 - 11900)/19 = 5950

V(t) = 124950 - 5950t

V(6) = 124950 - 5950(6)

V(6) = your answer