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D=32(1.16)^((q)/(4)) The given equation models the total number of downloads in thousands, D, of a mobile game q quarter years after it officially launches. Based on the model, which of the following statements is true? Choose 1 answer: (A) The number of total downloads increases by 16% each year. (B) The number of total downloads increases by 64% each year. (C) The number of total downloads increases by 16% each quarter year. (D) The number of total downloads increases by 64% each quarter year.

D=32(1.16)q4 D=32(1.16)^{\frac{q}{4}} \newlineThe given equation models the total number of downloads in thousands, D D , of a mobile game q q quarter years after it officially launches. Based on the model, which of the following statements is true?\newlineChoose 11 answer:\newline(A) The number of total downloads increases by 16% 16 \% each year.\newline(B) The number of total downloads increases by 64% 64 \% each year.\newline(C) The number of total downloads increases by 16% 16 \% each quarter year.\newline(D) The number of total downloads increases by 64% 64 \% each quarter year.

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Q. D=32(1.16)q4 D=32(1.16)^{\frac{q}{4}} \newlineThe given equation models the total number of downloads in thousands, D D , of a mobile game q q quarter years after it officially launches. Based on the model, which of the following statements is true?\newlineChoose 11 answer:\newline(A) The number of total downloads increases by 16% 16 \% each year.\newline(B) The number of total downloads increases by 64% 64 \% each year.\newline(C) The number of total downloads increases by 16% 16 \% each quarter year.\newline(D) The number of total downloads increases by 64% 64 \% each quarter year.
  1. Analyze Equation: Analyze the given equation.\newlineThe equation provided is D=32(1.16)(q/4)D=32(1.16)^{(q/4)}. This equation models the total number of downloads in thousands, DD, of a mobile game qq quarter years after it officially launches. The base of the exponent, 1.161.16, suggests a growth factor. To understand what this growth factor represents, we need to consider how it is applied in the equation.
  2. Determine Growth Period: Determine the growth period.\newlineThe exponent q/4q/4 indicates that the growth factor of 1.161.16 is applied every quarter year because qq is divided by 44. This means that the growth rate is compounded quarterly, not annually.
  3. Identify Growth Rate: Identify the growth rate.\newlineSince the base of the exponent is 1.161.16, this means that each quarter year, the total number of downloads increases by 16%16\%. This is because a growth factor of 1.161.16 corresponds to a 16%16\% increase from the previous amount.
  4. Choose Correct Answer: Choose the correct answer.\newlineBased on the analysis, the correct statement about the model is that the number of total downloads increases by 16%16\% each quarter year. Therefore, the correct answer is (C) The number of total downloads increases by 16%16\% each quarter year.

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