SOLUTION: After T years, the value of a car purchased for $20,000 is v=20,000(.75)^T When will this car be worth $500.00?

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Question 61857: After T years, the value of a car purchased for $20,000 is
v=20,000(.75)^T
When will this car be worth $500.00?
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(48558) About Me  (Show Source):
You can put this solution on YOUR website!
After T years, the value of a car purchased for $20,000 is
v=20,000(.75)^T
When will this car be worth $500.00?
-------------
500=20000(0.75)^T
1/40 = 0.75^T
Take the log of both sides to get:
-1.60206=T(-0.1249387366)
T=12.82 years.
Cheers,
Stan H.

Answer by josmiceli(6785) About Me  (Show Source):
You can put this solution on YOUR website!
500+=+2%2A10%5E4%2A%28.75%29%5Et
.75%5Et+=+5%2A10%5E2+%2F%282%2A10%5E4%29
.75%5Et+=+25%2A10%5E-3
t%2Alog%28.75%29+=+log%2825%29+%2B+%28-3%29
-.125t+=+1.398+-+3
.125t+=+1.602
t+=+12.82
The car will be worth $500 in about 12 years 8 months