Exponential Depreciation

initial value is $1500 that looses .5% of its value each month.

what is the expression for the value V(t) of the asset after t years?

Question

Exponential Depreciation 

initial value is $1500 that looses .5% of its value each month. 

what is the expression for the value V(t) of the asset after t years?

tkhunny · Answer

One Year: 1500 - 0.005*1500 = 1500(1 - 0.005) = 1500(0.995)
What does this suggest for multiple years?

rajee_sam · Answer

V(t) = 1500 (.995)^t

tkhunny · Answer

I guess we'll never know if our friend from Nebraska will be able to figure it out.

anonymous · Answer

rajee-where did hte .995 come from?

tkhunny · Answer

Did you read the first response to your post?

anonymous · Answer

gottcha- i was just blanking, and trying to move the 1500. to solve for t 

but if it's for each month doesn't something have to be divided by 12? 

I thought that the t had to be specific and was usually in years?

rajee_sam · Answer

rate of depreciation will be 1-.005 = .995

rajee_sam · Answer

If it is was rate of appreciation then 1+.005 = 1.005

anonymous · Answer

and where does the exponential go? shouldn't it be 1500e^(.995t)

tkhunny · Answer

@huskerfan12 Good call.  We both missed it.

$V(t) = 1500*(0.995)^{Months} = 1500*(0.995)^{Years/12} = = 1500*(0.995)^{t/12}$

tkhunny · Answer

Silly formatting!

$V(t) = 1500\cdot (0.995)^{t/12}$

anonymous · Answer

what about the exponential fn?

rajee_sam · Answer

it is of the type Y = ab^x Where y is the function, a is the initial value and b^x is the exponent.

rajee_sam · Answer

b is the rate and x is the period

tkhunny · Answer

I never did like that.  Someone decide we should ALWAYS use $e^{something}$, probably due to its relationship to differential equations.  I strongly disagree with this convention.  $0.995^{Something}$ is just as valid.

Anyway, just solve for it.  $0.995 = e^{k}$ and you will have your form $V(t) = 1500\cdot e^{k(t/12)}$

rajee_sam · Answer

sorry Huskerfan tk is right in a way. my bad. the function is V(t) = 1500(.995)^12t and not t/12 because the rate is per month so for a year it should be times 12

anonymous · Answer

so should it be t12 or t/12?

rajee_sam · Answer

sorry again it is t/12

rajee_sam · Answer

go with tk

tkhunny · Answer

Month = Year / 12

rajee_sam · Answer

Well done hunny you are absolutely right

rajee_sam · Answer

Husker use tk's answer