Question 530·Easy·Math

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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 a function, an ordered pair lists the input first and the output second. Use the units to identify which quantity is the input, then evaluate that value in Desmos to check the pair. Keep the distance and intensity in their assigned places. Swapping them changes what the pair says.

Hints

Hint 1
An ordered pair for a function has the form $(\text{input},\text{output})$ . Here, distance $d$ is the input, measured in meters. Which coordinate of $(3,200)$ represents distance?
Hint 2
The output $I(d)$ is intensity, measured in lux. To check the pair, put its first coordinate into the function. What does Desmos give for $I(3)$ ?

Step-by-step

Read the input, then check the output
Step 1
Assign the coordinates their units
The rule takes distance $d$ in meters as its input and gives intensity in lux as its output. So in $(3,200)$ , $3$ is the proposed distance and $200$ is the proposed intensity. The distance $3$ is allowed because $1\le d\le 10$ .
Step 2
Check the intensity at 3 meters
Type $I(d)=\frac{1800}{d^2}$ on one line and $I(3)$ on the next. Desmos prints $200$ . Evaluating $I(3)$ means putting $3$ in for $d$ , so the pair agrees with the rule.
Step 3
State what the pair means
The pair says that at 3 meters from the source, the intensity is 200 lux. Don't reverse the coordinates: $200$ meters is outside the given distance range. Choice D.

Lessons that teach this

SAT Nonlinear FunctionsIntermediateCoreEvaluate nonlinear functions and recover inputs

Question 530·Easy·Math

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