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$f(x)=10(1.25)^x$ $\newline$ 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? $\newline$ Choose $1$ answer: $\newline$ (A) $\$$ $15$ . $63$ $\newline$ (B) $\$$ $16$ . $39$ $\newline$ (C) $\$$ $93$ . $13$ $\newline$ (D) $\$$ $867$ . $36$

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Find a value using two-variable equations: word problems

Full solution

Q.

f(x)=10(1.25)^x

\newline

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?

\newline

Choose

1

answer:

\newline

(A)

\$

15

.

63

\newline

(B)

\$

16

.

39

\newline

(C)

\$

93

.

13

\newline

(D)

\$

867

.

36

Identify Function and Value: Identify the given function and the value to substitute for $x$ . $\newline$ The function given is $f(x) = 10(1.25)^x$ , which models the price of a rare trading card in dollars $x$ years after its initial release. We need to find the price $20$ years after its initial release, so we will substitute $x$ with $20$ .
Substitute in Function: Substitute $x$ with $20$ in the function. $f(20) = 10(1.25)^{20}$ Now we need to calculate the value of $1.25$ raised to the power of $20$ and then multiply it by $10$ .
Calculate Exponential Value: Calculate $1.25^{20}$ . Using a calculator, we find that $1.25^{20}$ is approximately $86.736$ .
Multiply by Constant: Multiply the result from Step $3$ by $10$ to find the price of the trading card. $\newline$ $f(20) = 10 \times 86.736$ $\newline$ $f(20) = 867.36$
Match with Answer Choices: Match the result to the given answer choices. $\newline$ The calculated price of the trading card $20$ years after its initial release is $\$867.36$ , which corresponds to answer choice (D).

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