The value, in dollars, of a used laptop years after it was purchased is modeled by the function Which of the following is the best interpretation of the ordered pair in this context?

Solution available with step-by-step explanation

SAT Nonlinear Functions Question 4 | Free SAT Prep | Aniko

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Question 4·Easy·Nonlinear Functions

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The value, in dollars, of a used laptop $t$ years after it was purchased is modeled by the function

V(t)=800(0.75)^{t},\qquad 0\le t\le 8.

Which of the following is the best interpretation of the ordered pair $(2,450)$ in this context?

For questions asking you to interpret an ordered pair or a point on a graph, first identify what the input and output of the function represent in the context (for example, time vs. value). Then remember that an ordered pair is always in the form (input, output), or here $(t, V(t))$ . Convert each number into its real-world meaning using the units given, and be careful not to reverse the coordinates or turn a single point into a rate or a starting value.

Hints

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Match variables to the context

Look at the function definition: what does $t$ stand for, and what does $V(t)$ stand for, in words?

Interpret the ordered pair format

For a function $V(t)$ , an ordered pair is written as $(t, V(t))$ . In $(2,450)$ , which number must be $t$ , and which number must be $V(t)$ ?

Put the math into a sentence

Once you know what $t=2$ and $V(t)=450$ each represent, combine them into a single sentence that describes the situation with time and value.

Desmos Guide

Enter the function

In Desmos, type f(x) = 800*(0.75)^x to represent the value of the laptop as a function of time in years.

Evaluate the function at 2 years

Either type f(2) in a new line or tap on the graph at $x=2$ . Look at the corresponding $y$ -value; that $y$ -value is the laptop’s value (in dollars) 2 years after purchase, which matches the second coordinate in the ordered pair $(2,450)$ .

Step-by-step Explanation

Identify what the variables mean in the function

The function is $V(t)=800(0.75)^t$ .

$t$ represents time in years after the laptop was purchased.
$V(t)$ represents the value of the laptop in dollars at time $t$ . So, any ordered pair $(t,V(t))$ tells you a time and the corresponding value of the laptop.

Understand what an ordered pair on this function represents

In general, for a function $y=f(x)$ , an ordered pair $(a,b)$ on the graph means that when the input is $x=a$ , the output is $y=b$ .

Here, the function is $V(t)$ , so an ordered pair $(2,450)$ means:

The input $t$ is $2$ (time in years).
The output $V(t)$ is $450$ (value in dollars).

Translate the ordered pair into a sentence in context

Putting the pieces together:

$t=2$ means 2 years after the laptop was purchased.
$V(t)=450$ means the value of the laptop is about $450.

So $(2,450)$ means that the laptop’s value is about $450 two years after it was purchased.

Strategy

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Desmos Guide

Step-by-step Explanation

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Strategy

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Desmos Guide

Step-by-step Explanation