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

$$ 15000$ $$15000$

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

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

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

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

Original: $14211.445344 \times 1.058 = $ 15035.709174$ $14211.445344 xx 1.058= $15035.709174$

to nearest $$ 100$ $$100$
$= $ 15000$ $=$15000$

-Fish

Answer 2 · 2018-02-27T01:48:39

Write an equation to satisfy the word problem:

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

Solve:

$0.7874 x = 12000$ $0.7874x=12000$

$x \approx 15240.03$ $x~~15240.03$

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