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

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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

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Given function: We are given the function A(q) = 86(0.9)^(q/4), which models the number of active players in thousands, q quarter years after 2018. We want to find out how long it takes for the number of active players to decrease by 10%. A decrease of 10% means the number of active players becomes 90% of the original number.Calculate 90%: To find out when the number of active players decreases by 10%, we need to solve for q when A(q) is 90% of the initial value. The initial value of A is 86, so 90% of 86 is 0.9 * 86.Set up equation: Calculate 90% of the initial value: 0.9 * 86 = 77.4. This means we are looking for the value of q that makes A(q) equal to 77.4.Isolate exponential term: Set up the equation 77.4 = 86(0.9)^(q/4) to solve for q.Calculate left side: Divide both sides of the equation by 86 to isolate the exponential term: 77.4 / 86 = (0.9)^(q/4).Deduce value of q: Calculate the left side of the equation: 77.4 / 86 = 0.9.Solve for q: Now we have 0.9 = (0.9)^(q/4). Since the bases are the same and the equation is of the form a = a^(x), we can deduce that x must be 1 for the equation to hold true. Therefore, q/4 = 1.Calculate final q: Multiply both sides of the equation by 4 to solve for q: q = 4 * 1.Calculate the value of q: q = 4.

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