A computer’s resale price, in dollars, years after it was purchased, is modeled by the function According to the model, what is the computer’s resale price years after it was purchased?

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SAT Nonlinear Functions Question 62 | Free SAT Prep | Aniko

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Question 62·Medium·Nonlinear Functions

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A computer’s resale price, in dollars, $x$ years after it was purchased, is modeled by the function

P(x)=1500(0.8)^{x/2}

According to the model, what is the computer’s resale price $4$ years after it was purchased?

For exponential models on the SAT, first identify what input value the question is asking for (here, the time in years), then substitute that value directly into the function. Simplify the exponent before calculating the power, then multiply by the coefficient. Always do a quick reasonableness check: if the base is less than 1, the output must be less than the initial amount, which helps you quickly eliminate impossible answer choices.

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Identify what the function gives you

The function $P(x)=1500(0.8)^{x/2}$ gives the resale price after $x$ years. What value of $x$ matches "4 years after it was purchased"?

Simplify the exponent before anything else

After substituting $x=4$ , you get $(0.8)^{4/2}$ . What is $4/2$ ? Replace the exponent with that simpler number.

Estimate the size of the answer

When you raise $0.8$ to a positive power and then multiply by $1500$ , should the result be greater than or less than $1500$ ? Use this to rule out impossible answer choices.

Desmos Guide

Evaluate the expression directly

Type 1500*(0.8)^(4/2) into Desmos exactly as written and press Enter. The value that Desmos outputs is the resale price after 4 years; match this number to one of the answer choices.

Step-by-step Explanation

Substitute the given time into the function

The resale price after $x$ years is given by

P(x)=1500(0.8)^{x/2}

We want the price $4$ years after purchase, so substitute $x=4$ :

P(4)=1500(0.8)^{4/2}

Simplify the exponent and evaluate the power

First simplify the exponent $4/2$ :

P(4)=1500(0.8)^{4/2}=1500(0.8)^2

Now compute $(0.8)^2$ :

(0.8)^2=0.8\times 0.8=0.64

So the expression becomes

P(4)=1500\times 0.64

Multiply to find the resale price

Now multiply $1500$ by $0.64$ :

1500\times 0.64=960

So, according to the model, the computer’s resale price 4 years after it was purchased is $960.

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Desmos Guide

Step-by-step Explanation

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Desmos Guide

Step-by-step Explanation