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A company has the goal of doubling their revenue from $\$$ $32$ million to $\$$ $64$ million over the next $2$ years. If the company increases its revenue by $50$ `%` in the first year, by approximately what percentage must the company increase their revenue in the second year in order to reach their goal?

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Exponential growth and decay: word problems

Full solution

Q. A company has the goal of doubling their revenue from

\$

32

million to

\$

64

million over the next

2

years. If the company increases its revenue by

50

`%` in the first year, by approximately what percentage must the company increase their revenue in the second year in order to reach their goal?

Calculate Revenue First Year: Calculate the revenue at the end of the first year. $\newline$ The company increases its revenue by $50$ % in the first year. $\newline$ Initial Revenue = $\$32$ million $\newline$ Percentage Increase = $50\%$ $\newline$ Revenue at the end of the first year = Initial Revenue + (Percentage Increase $\times$ Initial Revenue) $\newline$ = $\$32$ million + $(0.50 \times \$32$ million) $\newline$ = $\$32$ million + $\$16$ million $\newline$ = $\$48$ million
Calculate Required Revenue Second Year: Calculate the required revenue at the end of the second year to meet the goal. $\newline$ The goal is to double the initial revenue, which is from $\$32$ million to $\$64$ million. $\newline$ Required Revenue at the end of the second year = $\$64$ million
Calculate Additional Revenue Second Year: Calculate the additional revenue needed in the second year to reach the goal. $\newline$ Additional Revenue needed = Required Revenue at the end of the second year - Revenue at the end of the first year $\newline$ = $\$64\,\text{million}$ - $\$48\,\text{million}$ $\newline$ = $\$16\,\text{million}$
Calculate Percentage Increase Second Year: Calculate the percentage increase needed in the second year. $\newline$ Percentage Increase needed = $(\text{Additional Revenue needed} / \text{Revenue at the end of the first year}) \times 100\%$ $\newline$ = $(\$16 \text{ million} / \$48 \text{ million}) \times 100\%$ $\newline$ = $0$ . $3333$ ... \times $100$ \% $\newline$ = $33$ . $33$ ...\%

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