The light intensity, in lux, measured at a distance meters from a small point source 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 133 | Free SAT Prep | Aniko

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Question 133·Easy·Nonlinear Functions

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The light intensity, in lux, measured at a distance $d$ meters from a small point source is modeled by the function

I(d)=\frac{1800}{d^2},\qquad 1\le d\le 10.

Which of the following is the best interpretation of the ordered pair $(3,200)$ in this context?

For function-interpretation questions, start by identifying what the input and output represent, including their units. Remember that in an ordered pair from a function, $(x,y)$ is always (input, output), so map the first coordinate to the input quantity and the second to the output quantity. Then quickly eliminate options that swap the roles, use the wrong units, or treat a single point as a statement about all inputs; the remaining choice that matches both order and units is correct.

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Match variables to real-world quantities

Look at the function definition. What real-world quantity does $d$ represent, and what real-world quantity does $I(d)$ represent?

Recall how ordered pairs work for functions

In a function, does the first coordinate represent the input or the output? What about the second coordinate?

Connect the numbers to their units

In the pair $(3,200)$ , which number should be measured in meters, and which should be measured in lux, based on how the function is defined?

Eliminate options that reverse or ignore roles

Check each answer choice: Does it correctly treat the first number as the distance and the second number as the intensity, with the proper units?

Desmos Guide

Enter the function

In Desmos, type y = 1800/x^2 to represent the light intensity function $I(d) = \frac{1800}{d^2}$ , with $x$ playing the role of $d$ .

Check the point corresponding to distance 3

Add a table in Desmos, put 3 in the $x$ column, and observe the corresponding $y$ -value. Interpret this as the intensity (in lux) at a distance of 3 meters from the source, and then match that interpretation with the correct answer choice.

Step-by-step Explanation

Identify what each variable represents

The function is

I(d) = \frac{1800}{d^2}

The problem states that:

$d$ is the distance from the light source, measured in meters.
$I(d)$ is the light intensity, measured in lux.

So, for this function, input $d$ (first coordinate) is a distance, and output $I(d)$ (second coordinate) is an intensity.

Understand what an ordered pair from this function means

An ordered pair from this function has the form $(d, I(d))$ .

That means:

The first number in the pair is a distance in meters.
The second number is the corresponding intensity in lux at that distance.

So when you see a pair like $(\text{something}, \text{something})$ , read it as:

At a distance of [first number] meters, the measured intensity is [second number] lux.

Apply this to the specific ordered pair and match the choice

Now apply the general meaning to $(3,200)$ :

The first coordinate, $3$ , is the distance in meters.
The second coordinate, $200$ , is the intensity in lux.

So $(3,200)$ means:

At a distance of 3 meters from the source, the measured intensity is 200 lux.

This matches answer choice D exactly.

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