The value of a $20,000 car decreases every, t. The equation below model this situation.
20,000(1-0.04t) = 13,000
How many years will the car be worth $13,000? Round to the nearest tenth if necessary.
I got 20,000(.96t)= 13,000, but I don't believe gives me the correct answer. Help!
typo - Damon, Saturday, April 21, 2012 at 8:26pm
this does not make sense:
" decreases every, t "
did it say it decreased 4% per year?
that would mean
.96^n =13/20
.96^n = .65
n log .96 = log .65
n = -.187/-.0177
= 10.6 years
math - Jane, Saturday, April 21, 2012 at 9:38pm
I understand most of the explanation except the part below:
n log .96 = log .65
n = -.187/-.0177
The answer is 10.6, but I don't know how to get passed .96t = .65. Please continue to help me. Thanks
To get from .96t = .65 to the solution of n = 10.6, we can use logarithms.
First, let's isolate t in the equation .96t = .65. Divide both sides of the equation by .96:
t = .65 / .96
Now, we can use logarithms to solve for t. Taking the logarithm (base 10) of both sides of the equation, we have:
log(t) = log(.65 / .96)
Using the quotient rule of logarithms, we can rewrite the right side of the equation:
log(t) = log(.65) - log(.96)
Now, we can evaluate the logarithmic expressions using a calculator:
log(t) = -0.1862 - (-0.0173)
log(t) = -0.1862 + 0.0173
log(t) = -0.1689
To solve for t, we need to find the antilogarithm (or inverse logarithm) of both sides of the equation:
t = antilog(-0.1689)
Using a calculator, we can find that the antilogarithm of -0.1689 is approximately 0.635.
Therefore, t is approximately 0.635.
However, please note that the original problem asks for the number of years, so we need to multiply t by 12 (since there are 12 months in a year) to convert it to years:
n = t * 12
n = 0.635 * 12
n = 7.62
Rounding to the nearest tenth, the car will be worth $13,000 after approximately 7.6 years.