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o-na [289]
3 years ago
10

A car purchased for $34,000 is expected to lose value, or depreciate, at a rate of 6% per year. Using x for years and y for the

value of the car, write the equation that models this situation. After how many years is the car first worth less than $21,000
Mathematics
1 answer:
lilavasa [31]3 years ago
7 0
The equation is y=34000(1-0.06)ˣ.

It will take nearly 8 years for the car to lose enough value to be worth less than $21,000.

Using 21,000 for y, we have
21000=34000(1-0.06)ˣ
21000=34000(0.94)ˣ

Dividing both sides by 34000:
21000/34000 = 34000(0.94)ˣ/34000
(21/34) = 0.94ˣ

Using logarithms to solve this,
\log_{0.94}(\frac{21}{34})=x
\\x=7.79 \approx8
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