R=380(1.08)^(t) The given equation models the revenue in thousands of dollars, R, of a company t years after 2012 . Of the following, which equation models the revenue of the company q quarters after 2012 ? Choose 1 answer: (A) R=380(1.02)^(4q) (B) quad R=380(1.36)^(q) (c) R=380(1.08)^((q)/(4)) (D) R=380(1.08)^(4q)

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R=380(1.08)^(t) The given equation models the revenue in thousands of dollars,  R, of a company  t years after 2012 . Of the following, which equation models the revenue of the company  q quarters after 2012 ? Choose 1 answer: (A)  R=380(1.02)^(4q) (B)  quad R=380(1.36)^(q) (c)  R=380(1.08)^((q)/(4)) (D)  R=380(1.08)^(4q)

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Convert Annual Growth Rate: We need to convert the given annual growth rate to a quarterly growth rate since there are 4 quarters in a year. The annual growth rate is 8% or 1.08 as a multiplier. To find the quarterly growth rate, we take the fourth root of 1.08 because we want to know how much it grows each quarter to end up with an 8% growth after 4 quarters.Calculate Quarterly Growth Rate: Calculating the fourth root of 1.08 can be done by raising 1.08 to the power of 1/4. This gives us the quarterly growth factor.Adjust Exponent for Quarters: Using a calculator, we find that 1.08^(1/4) is approximately 1.0194, which is about a 1.94% quarterly growth rate. However, we can simplify this by recognizing that a 2% quarterly growth rate would be close enough for the options given, which is 1.02 as a multiplier.Match with Answer Choices: Now we need to adjust the exponent in the original equation to reflect the number of quarters instead of years. Since there are 4 quarters in a year, we multiply the number of quarters, q, by 4 to get the equivalent number of quarters for t years. The new equation should have the form R = 380(1.02)^(4q).Looking at the answer choices, option (A) R = 380(1.02)^(4q) matches our derived equation and represents the revenue R in thousands of dollars q quarters after 2012.

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