SOLUTION: The initial value of a vehicle is 25000 each year it depreciates V=25000(0.8)^t Will the car ever be worth nothing? Thanks

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Question 1194551: The initial value of a vehicle is 25000 each year it depreciates V=25000(0.8)^t Will the car ever be worth nothing?

Thanks
Found 3 solutions by ikleyn, MathLover1, MathTherapy:
Answer by ikleyn(52813) About Me  (Show Source):
You can put this solution on YOUR website!
.

When the depreciated value of the car will become less than half-cent,
it will be worth nothing (after rounding the value).


Simply the given exponential formula becomes non-sensical and non-applicable
much earlier than the time becomes infinite.



Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The initial value of a vehicle is 25000 each year it depreciates
V=25000%280.8%29%5Et+
Will the car ever be worth nothing? -> will be when V=0

0=25000%280.8%29%5Et+.........solve for t
0%2F25000=%280.8%29%5Et+
0=%280.8%29%5Et+.......take log of both sides
log%280%29=log%28%280.8%29%5Et%29+=> log%2810.0%29=+-infinity
infinity=t%2Alog%280.8%29+
t=+-infinity%2F-0.2231435513142097+
t=+infinity+-> no solution for t in R


Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

The initial value of a vehicle is 25000 each year it depreciates V=25000(0.8)^t Will the car ever be worth nothing?
Thanks
Looking at the right side of the equation, it's obvious that NO value for "t" could ever make the left-side, 0. It will be close to, 

but never 0. Plus, "t" (time) can never be < 0.