Question 674·Easy·Math

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The vertical height, in meters, of a drone above its launch point is modeled by the function $s$ , where

s(t) = 5t^2,

and $t$ is the time in seconds since liftoff.

Which of the following is the best interpretation of $s(6)=180$ in this context?

In function notation, the number in parentheses is the input, and the value after the equals sign is the output. For a height model, match each number to the quantity and unit the question assigns it; define and evaluate the function in Desmos if you want to check the value. Don't mistake a height at one moment for a per-second speed.

Hints

Hint 1
In function notation, $s(6)$ means put $6$ in for the time $t$ . Since $t$ counts seconds since liftoff, what moment of the drone's flight does that input identify?
Hint 2
A function's output has the units assigned to the function, not the input. Which quantity does $s(t)$ measure, and which does $t$ measure? Keep those units attached as you read the statement.

Step-by-step

Read the input and output with units
Step 1
Identify what the input means
In function notation, $s(6)$ means use $6$ for $t$ . Since $t$ measures seconds since liftoff, the input identifies 6 seconds after launch, not a height or a repeating interval.
Step 2
Evaluate and interpret the output
Type $s(t)=5t^2$ , then $s(6)$ on the next line. Desmos displays $180$ . The problem defines $s$ as height in meters, so $180$ is a height, not a speed. A function's output describes the quantity at that input. After $6$ seconds, the drone is $180$ meters above its launch point. Choice D.

Question 674·Easy·Math

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