Question

A business uses straight-line depreciation to determine the value y of an automobile over a 5-year period. Suppose the original value (when t=0) is equal to $14,500 and the salvage value (when t=5) is equal to $4,000.
a) By how much has the automobile depreciated over the 5 years?
b) By how much is the value of the automobile reduced at the end of each of the 5 years?
c) Write the linear equation that models the value s of this automobile at the end of year t.

Answer 1

For this problem. it is found that:

a) The automobile has depreciated 75% in 5 years.

b) The value of the automobile was reduced by $10,500 in five years.

c) The linear function is: s(t) = 14,500 - 2,100t.

What is a linear function?

A linear function is modeled by:

y = ax + b

In which:

• a is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

• b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

From the problem, we have that:

a) The automobile has depreciated 75% in 5 years, as 4000/14500 = 0.25, and 100% - 25% = 75%.

b) The value of the automobile was reduced by $10,500 in five years, as 14500 - 4000 = $10,500.

For the linear function, we have that:

• The initial value is b = 14500.

• The slope is of a = -10500/5 = -2100.

Hence the linear function is: s(t) = 14,500 - 2,100t.

More can be learned about linear functions at brainly.com/question/24808124

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