exponential fcns and applications: declining-balance method of depreciation (crane)

E

ect

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The declining-balance method of depreciation is an accounting method businesses use to deduct most of the cost of new equipment during the first few years of purchase. Unlike other methods, the declining-balance formula does not consider salvage value. For the value of a crane, the function

V(t)=400000(1−0.35)^t
where V is value and t is time in years, can be used to find the value of the crane for the first 9 years of use.

What is the value if the crane after 4years and 9months?


I don't understand how to find the value after 4 years and 9 months and I'm not sure what I'm doing wrong when calculating it I think its either my method or the wrong value for t.
 
One month is 1/12 of a year, so what fraction of a year is 9 months? How would you express that as a decimal? Then how would you express "4 years and 9 months?" What happens if you plug that t value into the function V(t)?
 
9 months would be 9/12 which is simplified to 3/4=0.75 so then 4 years and 9 months would be 4.75
 
plugged in, the crane would have a value of 51,689.03632
 
Yes. That's the same value that I get. The only minor thing I'd do differently is round it to two decimal places, since V(t) represents value, so you can have dollars and cents. But otherwise, good job.
 
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