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Rafael purchased his car for $\$12,000$ . The value of Rafael's car depreciates over time, decreasing by $10\%$ every year. Which of the following graphs could model this relationship if $t$ is elapsed time in years, and $V$ is the value of Rafael's car in thousands of dollars?

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Evaluate two-variable equations: word problems

Full solution

Q. Rafael purchased his car for

\$12,000

. The value of Rafael's car depreciates over time, decreasing by

10\%

every year. Which of the following graphs could model this relationship if

t

is elapsed time in years, and

V

is the value of Rafael's car in thousands of dollars?

Understand the problem: Step $1$ : Understand the problem. $\newline$ Rafael's car initially costs $\$12,000$ , which is $12$ in thousands of dollars. It depreciates by $10\%$ annually. $\newline$ We need to find a graph that shows this decrease in value over time.
Calculate initial value: Step $2$ : Calculate the value after one year. $\newline$ Initial value = $12$ thousand dollars. $\newline$ Depreciation = $10\%$ of $12 = 1.2$ thousand dollars. $\newline$ Value after one year = $12 - 1.2 = 10.8$ thousand dollars.
Check consistency: Step $3$ : Check the pattern for another year to ensure consistency. Value after second year = $10.8 - (10\% \text{ of } 10.8) = 10.8 - 1.08 = 9.72$ thousand dollars.
Identify graph type: Step $4$ : Identify the type of graph. $\newline$ The value decreases by a fixed percentage each year, which is characteristic of an exponential decay model. $\newline$ The graph should show a decreasing curve, not a straight line.

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