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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?

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?

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Full solution

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?
  1. Identify Function & Value: Identify the function and the value of xx to substitute. The function given is f(x)=10(1.25)xf(x) = 10(1.25)^x, and we need to find the price 2020 years after 19931993, so x=20x = 20.
  2. Substitute x=20x = 20: Substitute x=20x = 20 into the function to find f(20)f(20). Calculate f(20)=10(1.25)20f(20) = 10(1.25)^{20}.
  3. Compute (1.25)20(1.25)^{20}: Use a calculator to compute (1.25)20(1.25)^{20}. The result is approximately 86.737886.7378.
  4. Multiply by 1010: Multiply the result by 1010 to get the final price. f(20)=10×86.7378=867.378f(20) = 10 \times 86.7378 = 867.378.

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