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f(x)=10(1.25)^(x) The function models f, the price of a rare trading card in dollars x years after its initial release in 1993. Based on the model, what is the price of the trading card 20 years after its initial release? Choose 1 answer: (A) $15.63 (B) $16.39 (c) $93.13 (D) $867.36

f(x)=10(1.25)x f(x)=10(1.25)^{x} \newlineThe function models f f , the price of a rare trading card in dollars x x years after its initial release in 19931993 . Based on the model, what is the price of the trading card 2020 years after its initial release?\newlineChoose 11 answer:\newline(A) $15.63 \$ 15.63 \newline(B) $16.39 \$ 16.39 \newline(C) $93.13 \$ 93.13 \newline(D) $867.36 \$ 867.36

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Q. f(x)=10(1.25)x f(x)=10(1.25)^{x} \newlineThe function models f f , the price of a rare trading card in dollars x x years after its initial release in 19931993 . Based on the model, what is the price of the trading card 2020 years after its initial release?\newlineChoose 11 answer:\newline(A) $15.63 \$ 15.63 \newline(B) $16.39 \$ 16.39 \newline(C) $93.13 \$ 93.13 \newline(D) $867.36 \$ 867.36
  1. Identify function and value: Identify the given function and the value to substitute for xx.\newlineThe function given is f(x)=10(1.25)xf(x) = 10(1.25)^x, and we need to find the price of the trading card 2020 years after its initial release, so we will substitute xx with 2020.
  2. Substitute xx with 2020: Substitute xx with 2020 in the function f(x)=10(1.25)xf(x) = 10(1.25)^x.\newlinef(20)=10(1.25)20f(20) = 10(1.25)^{20}
  3. Calculate (1.25)20(1.25)^{20}: Calculate the value of (1.25)20(1.25)^{20}.(1.25)20=1.2520(1.25)^{20} = 1.25^{20} Using a calculator, we find that 1.2520≈86.7361.25^{20} \approx 86.736
  4. Multiply by 1010: Multiply the result from Step 33 by 1010 to find the price of the trading card.f(20)=10×86.736f(20) = 10 \times 86.736f(20)≈867.36f(20) \approx 867.36
  5. Match with given options: Match the result with the given options.\newlineThe result from Step 44 is $867.36\$867.36, which corresponds to option (D).

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