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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%15\% per year until 22 years ago, when it started to grow by $179.5\$179.5 million per year. If the sales tax revenue 22 years ago was $2.1\$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%15\% per year?\newline(Note: 11 billion =1,000=1,000 million)\newlineChoose 11 answer:\newline(A) $136\$136 million\newline(B) $318\$318 million\newline(C) $2.05\$2.05 billion\newline(D) $5.24\$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%15\% per year until 22 years ago, when it started to grow by $179.5\$179.5 million per year. If the sales tax revenue 22 years ago was $2.1\$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%15\% per year?\newline(Note: 11 billion =1,000=1,000 million)\newlineChoose 11 answer:\newline(A) $136\$136 million\newline(B) $318\$318 million\newline(C) $2.05\$2.05 billion\newline(D) $5.24\$5.24 billion
  1. Calculate Initial Revenue: Let's first calculate what the sales tax revenue would be this year if it had continued growing by 1515\% per year. Two years ago, the revenue was $2.1\$2.1 billion. To find the revenue after one year with a 1515\% increase, we use the formula:\newlineRevenue after one year = Initial revenue ×(1+growth rate)\times (1 + \text{growth rate})
  2. Calculate Revenue After One Year: Calculating the revenue after one year with a 1515% increase:\newlineRevenue after one year = $2.1\$2.1 billion ×(1+0.15)\times (1 + 0.15)\newlineRevenue after one year = $2.1\$2.1 billion ×1.15\times 1.15\newlineRevenue after one year = $2.415\$2.415 billion
  3. Calculate Revenue After Two Years: Now, let's calculate the revenue after the second year with another 15%15\% increase: Revenue after two years = Revenue after one year ∗* (1+growth rate)(1 + \text{growth rate})
  4. Calculate Actual Revenue This Year: Calculating the revenue after two years with a 1515% increase:\newlineRevenue after two years = $2.415\$2.415 billion ×(1+0.15)\times (1 + 0.15)\newlineRevenue after two years = $2.415\$2.415 billion ×1.15\times 1.15\newlineRevenue after two years = $2.77725\$2.77725 billion
  5. Find the Difference: Next, we need to calculate the actual sales tax revenue for this year, which is growing by $179.5\$179.5 million per year instead of 15%15\%. Two years ago, the revenue was $2.1\$2.1 billion. So after two years of growing by $179.5\$179.5 million each year, the revenue would be:\newlineRevenue this year = Revenue two years ago + 2×2 \times Annual growth in millions
  6. Round the Difference: Calculating the actual revenue this year:\newlineRevenue this year = $2.1\$2.1 billion + 2×$179.52 \times \$179.5 million\newlineRevenue this year = $2.1\$2.1 billion + $359\$359 million\newlineRevenue this year = $2.459\$2.459 billion
  7. Round the Difference: Calculating the actual revenue this year:\newlineRevenue this year = $2.1\$2.1 billion + 2×$179.52 \times \$179.5 million\newlineRevenue this year = $2.1\$2.1 billion + $359\$359 million\newlineRevenue this year = $2.459\$2.459 billionNow we can find the difference between the revenue if it had grown by 15%15\% per year and the actual revenue growing by $179.5\$179.5 million per year:\newlineDifference = Revenue with 15%15\% growth - Actual revenue this year
  8. Round the Difference: Calculating the actual revenue this year:\newlineRevenue this year = $2.1\$2.1 billion + 2×$179.52 \times \$179.5 million\newlineRevenue this year = $2.1\$2.1 billion + $359\$359 million\newlineRevenue this year = $2.459\$2.459 billionNow we can find the difference between the revenue if it had grown by 15%15\% per year and the actual revenue growing by $179.5\$179.5 million per year:\newlineDifference = Revenue with 15%15\% growth - Actual revenue this yearCalculating the difference:\newlineDifference = $2.77725\$2.77725 billion - $2.459\$2.459 billion\newlineDifference = 2×$179.52 \times \$179.500 billion\newlineDifference = 2×$179.52 \times \$179.511 million
  9. Round the Difference: Calculating the actual revenue this year:\newlineRevenue this year = $2.1\$2.1 billion + 2×$179.52 \times \$179.5 million\newlineRevenue this year = $2.1\$2.1 billion + $359\$359 million\newlineRevenue this year = $2.459\$2.459 billionNow we can find the difference between the revenue if it had grown by 15%15\% per year and the actual revenue growing by $179.5\$179.5 million per year:\newlineDifference = Revenue with 15%15\% growth - Actual revenue this yearCalculating the difference:\newlineDifference = $2.77725\$2.77725 billion - $2.459\$2.459 billion\newlineDifference = 2×$179.52 \times \$179.500 billion\newlineDifference = 2×$179.52 \times \$179.511 millionSince we need to approximate, we can round the difference to the nearest million, which gives us:\newlineDifference 2×$179.52 \times \$179.522 million

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