An accountant for a certain state models the sales tax revenue that the state has earned over several years. The model shows that sales tax revenue grew by $15\%$ per year until $2$ years ago, when it started to grow by $\$179.5$ million per year. If the sales tax revenue $2$ years ago was $\$2.1$ billion, approximately how much lower is the sales tax revenue this year than it would be if it had continued growing by $15\%$ per year? (Note: $1$ billion $= 1,000$ million) $\newline$ Choose $1$ answer: $\newline$ (A) $\$136$ million $\newline$ (B) $\$318$ million $\newline$ (C) $\$2.05$ billion $\newline$ (D) $\$5.24$ billion

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Q. An accountant for a certain state models the sales tax revenue that the state has earned over several years. The model shows that sales tax revenue grew by

15\%

per year until

2

years ago, when it started to grow by

\$179.5

million per year. If the sales tax revenue

2

years ago was

\$2.1

billion, approximately how much lower is the sales tax revenue this year than it would be if it had continued growing by

15\%

per year? (Note:

1

billion

= 1,000

million)

\newline

Choose

1

answer:

\newline

(A)

\$136

million

\newline

(B)

\$318

million

\newline

(C)

\$2.05

billion

\newline

(D)

\$5.24

billion

Calculate Sales Tax Revenue: Calculate the sales tax revenue if it had continued growing by $15$ % per year for two years. $\newline$ Sales tax revenue $2$ years ago = $\$2.1$ billion $\newline$ Growth rate = $15\%$ per year $\newline$ Sales tax revenue if $15\%$ growth continued for $1$ year = $\$2.1$ billion $\times (1 + 0.15) = \$2.1$ billion $\times 1.15$
Continue First Year's Growth: Continue the calculation for the first year's growth. Sales tax revenue if $15$ % growth continued for $1$ year = $\$2.1$ billion $* 1.15 = \$2.415$ billion
Calculate Second Year's Growth: Calculate the sales tax revenue if the $15$ \% growth continued for the second year. $\newline$ Sales tax revenue if $15$ \% growth continued for $2$ years = $\$2.415$ billion $\times (1 + 0.15) = \$2.415$ billion $\times 1.15$
Continue Second Year's Growth: Continue the calculation for the second year's growth. Sales tax revenue if $15$ % growth continued for $2$ years = $\$2.415$ billion $* 1.15 \approx \$2.77725$ billion
Calculate Actual Revenue: Calculate the actual sales tax revenue for this year. $\newline$ Actual sales tax revenue $2$ years ago = $\$2.1$ billion $\newline$ Growth per year for the past $2$ years = $\$179.5$ million $\newline$ Actual sales tax revenue for this year = $\$2.1$ billion + $2$ * $\$179.5$ million
Continue Actual Revenue Calculation: Continue the calculation for the actual sales tax revenue. $\newline$ Actual sales tax revenue for this year = $\$2.1$ billion + $2$ * $\$179.5$ million = $\$2.1$ billion + $\$359$ million = $\$2.459$ billion
Calculate Revenue Difference: Calculate the difference between the projected sales tax revenue (if it had grown by $15$ % per year) and the actual sales tax revenue. $\newline$ Difference = Projected sales tax revenue - Actual sales tax revenue $\newline$ Difference = $\$2.77725$ billion - $\$2.459$ billion
Continue Difference Calculation: Continue the calculation for the difference. $\newline$ Difference = $\$2.77725$ billion - $\$2.459$ billion $\approx$ $\$318.25$ million