A business uses straightline depreciation to determine the v

A business uses straight-line depreciation to determine the value y of an automobile over a 6-year period. Suppose the original value (when t=0) is equal to $16,200 and the salvage value left (when t=6) is equal to $6000

a. By how much has the automobile depreciated over the 6 years?

b. By how much is the value of the automobile reduced at the end of each of the 6 years?

c. Write the linear equation that models the value s of this automobile at the end of year t.

Solution

original value = $16,200

after 6 years value = $ 6000

so, we have 2 points from this information

(0,16200)   and ( 6,6000)

standard linear function is given by the equation

y = mx+ b

m = slope = 6000 - 16200 / 6 - 0

m = -1700

a) the value has depreciated 1700*6 = $10200 over 6 years

b) every year value has reduced $ 1700

plugging one point and m into the standard equation

16200 = -1700(00 + b

b = 16200

therefore, linear model is

y = -1700 t + 16200

where t = time in years