Answer:
(a) (log X - log 25000)/log 0.85 = t
(b) about 9.9 years
Step-by-step explanation:
(a) Let X = value and t = elapsed years since purchase; X in dollars
X = 25000 x 0.85 x 0.85 x 0.85 ... with a factor of 0.85 for every year
(If you lose 15% of value, you have 85% left, right?)
So if you do it for t years, you have t as the exponent on the 0.85 factor.
is a good equation, but not logarithmic like they ask.
because the log of a product is the sum of the logs of the factors
log X = log 25000 + t*log 0.85 because the log of a power is power times log
log X - log 25000 = t* log 0.85 just algebra, subtracting from both sides
(log X - log 25000)/log 0.85 = t just algebra, dividing both sides
<u>(b)</u> If we let X = $5000
t = (log 5000 - log 25000)/log 0.85
= (3.69897 - 4.39794)/-0.07058
= 9.90
So t = 9.9 years is a good estimate