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The value of a machine was reduced by $36\%$ within $2$ years. What is the rate of depreciation per year? $\newline$ A. $6\%$ $\newline$ B. $18\%$ $\newline$ C. $20\%$ $\newline$ D. $36\%$

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Exponential growth and decay: word problems

Full solution

Q. The value of a machine was reduced by

36\%

within

2

years. What is the rate of depreciation per year?

\newline

A.

6\%

\newline

B.

18\%

\newline

C.

20\%

\newline

D.

36\%

Calculate Yearly Rate: First, we know the machine's value decreased by $36\%$ over $2$ years. To find the yearly rate, we divide the total percentage by the number of years. $\newline$ So, $36\% \div 2$ years = $18\%$ per year.
Verify Yearly Rate: Now, let's check if the answer makes sense. If the machine loses $18\%$ of its value each year, then over $2$ years, it would lose $18\% + 18\% = 36\%$ , which matches the given information.

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