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A company has the goal of doubling their revenue from $32$ million dollars to $64$ million dollars 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 dollars to

64

million dollars 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 First Year Revenue: Calculate the revenue after the first year with a $50$ % increase. $\newline$ First year revenue = Initial revenue + ( $50$ % of Initial revenue) $\newline$ = $32$ million + ( $0.5 \times 32$ million) $\newline$ = $32$ million + $16$ million $\newline$ = $48$ million dollars.
Determine Remaining Amount: Determine the remaining amount needed to reach the goal of $64$ million dollars. $\newline$ Remaining amount = Goal - First year revenue $\newline$ $= 64$ million - $48$ million $\newline$ $= 16$ million dollars.
Calculate Percentage Increase: Calculate the percentage increase needed in the second year. $\newline$ Percentage increase needed = $(\text{Remaining amount} / \text{First year revenue}) \times 100$ $\newline$ = $(16 \text{ million} / 48 \text{ million}) \times 100$ $\newline$ = $0.3333 \times 100$ $\newline$ = $33.33\%$ .

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