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I need help figuring out how to set this word problem up and to solve it:

 

A delivery truck is purchased new for $54,000. 

a. Write a linear function of the form y = mt + b to represent the value y of the vehicle t years after purchase. Assume that the vehicle is depreciated by $ 6750 per year. 

b. Suppose that the vehicle is depreciated so that it holds 70% of its value form the previous year. Write an exponential function of the form y = Vobt, where V0 is the initial value and t is the number of years after purchase. 

c. To the nearest dollar, determine the value of the vehicle after 4 yr and after 8 yr using the linear model. 

d. To the nearest dollar, determine the value of the vehicle after 4 yr and after 8 yr using the exponential model

 

I got :

 

a) -6750t+54000=y

b) y=54000(.70)t

c) 27,000 for 4 years, and $0 for 8 years

d) $12,965 for 4 years , and $3,113 for 8 years

 

I would appriciate any help. Are my answers correct? Am I doing the work right?

Guest Jul 30, 2018
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As far as I can see, everything looks OK, except for 4-year depreciations in c and d. You have them switched around. The 4-year depreciation using the exponential model would be: 0.7^4 x $54,000 =$12,965 in "c". The 4-year depreciation using the linear model would be: 54,000 - (4 x $6,750) =$27,000 in "d". And that is it. 

Guest Jul 30, 2018

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