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A(q)=86(0.9)^((q)/(4)) The function models A, the number of active players, in thousands, of a mobile game q quarter years after 2018. Based on the function, how many quarter years does it take for the number of active players to decreases by 10% ? Choose 1 answer: (A) 0.1 (B) 0.225 (c) 0.9 (D) 4

A(q)=86(0.9)q4 A(q)=86(0.9)^{\frac{q}{4}} \newlineThe function models A A , the number of active players, in thousands, of a mobile game q q quarter years after 20182018. Based on the function, how many quarter years does it take for the number of active players to decreases by 10% 10 \% ?\newlineChoose 11 answer:\newline(A) 00.11\newline(B) 00.225225\newline(C) 00.99\newline(D) 44

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Q. A(q)=86(0.9)q4 A(q)=86(0.9)^{\frac{q}{4}} \newlineThe function models A A , the number of active players, in thousands, of a mobile game q q quarter years after 20182018. Based on the function, how many quarter years does it take for the number of active players to decreases by 10% 10 \% ?\newlineChoose 11 answer:\newline(A) 00.11\newline(B) 00.225225\newline(C) 00.99\newline(D) 44
  1. Problem Understanding: Understand the problem.\newlineWe are given a function A(q)=86(0.9)q4A(q) = 86(0.9)^{\frac{q}{4}} that models the number of active players in thousands, qq quarter years after 20182018. We need to find out how long it takes for the number of active players to decrease by 10%10\%.
  2. Equation Setup: Set up the equation to solve for the time it takes for the number of active players to decrease by 1010%. We want to find the value of qq such that A(q)A(q) is 90%90\% of A(0)A(0), since a 10%10\% decrease means the number of players is 90%90\% of the original number. So, we set up the equation: 86(0.9)q4=0.9×8686(0.9)^{\frac{q}{4}} = 0.9 \times 86.
  3. Equation Simplification: Simplify the equation.\newlineDivide both sides of the equation by 8686 to isolate the exponential term:\newline(0.9)(q/4)=0.9(0.9)^{(q/4)} = 0.9.
  4. Solving for q: Solve for q.\newlineSince the bases are the same, we can set the exponents equal to each other:\newlineq4=1\frac{q}{4} = 1.
  5. Solving for q: Solve for q.\newlineSince the bases are the same, we can set the exponents equal to each other:\newlineq4=1\frac{q}{4} = 1.Multiply both sides by 44 to solve for q.\newlineq=4q = 4.

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