anonymous
  • anonymous
A companys car has an original value of $85000 and will be depreciated linearly over 6 years with scrap value of 10,000. A. Find the expression giving the book value of the car at the end of the year (0(equal to less than) t (equal to less than 6)
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
is it different because the previous one has a scrap value of 0 and the new one has a scrap value of 10000? On the new one the professor wrote v=c-r(t) but that confuses me because we didn't do that for the previous one
jim_thompson5910
  • jim_thompson5910
change in value = scrapValue - orginalValue change in value = 10,000 - 85,000 change in value = -75,000 change in time = (new year) - (old year) change in time = 6-0 change in time = 6 we have the item losing $75,000 over 6 years annual rate of depreciation = (change in value)/(Change in time) annual rate of depreciation = (-75,000)/(6) annual rate of depreciation = -12,500 so the car is losing $12,500 a year
jim_thompson5910
  • jim_thompson5910
book value = (starting value) + (rate of change)*(number of years) book value = (85,000) + (-12,500)*(t) book value = 85,000-12,500*t book value = -12,500*t + 85,000

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jim_thompson5910
  • jim_thompson5910
if I wanted to know the book value at the beginning, then I just plug t = 0 into the book value equation book value = -12,500*t + 85,000 book value = -12,500*0 + 85,000 ... replace t with 0 book value = 0+85,000 book value = 85,000 as we expect, the book value is $85,000 at the beginning of the car's lifespan
jim_thompson5910
  • jim_thompson5910
or...if I wanted to know the scrap value, plug in t = 6 since we're going to scrap it at the 6 year mark book value = -12,500*t + 85,000 book value = -12,500*6 + 85,000 ... replace t with 6 book value = -75,000+85,000 book value = 10,000 as we expect, the scrap value is $10,000 (the lowest we'll go in terms of keeping the vehicle) at the end of the car's lifespan
jim_thompson5910
  • jim_thompson5910
here's the graph https://www.desmos.com/calculator/l0wgunxhxn see the attached image

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