Joshua just purchased a 4-year-old car for $12,000. He was told that this make and model depreciates exponentially at a rate of 5.8% per year. What was the original price to the nearest hundred dollars?

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Answer 1 · 2018-02-27T01:28:54

$$15000$

After 4 years, the car is worth $$12000$ .
Work backwards.

$3$ $"years"=12000 xx 1.058= $12696$

$2$ $"years"= 12696 xx 1.058= $13432.368$

$1$ $"year"= 13432.368 xx 1.058= $14211.445344$

Original: $14211.445344 xx 1.058= $15035.709174$

to nearest $$100$
$=$15000$

-Fish

Answer 2 · 2018-02-27T01:48:39

Write an equation to satisfy the word problem:

$12000=x(1-0.058)^(4)$

Solve:

$0.7874x=12000$

$x~~15240.03$

The price was approximately $$15240.03$ , and to the nearest hundred dollars is $$15200$ .