Question 169·Easy·Nonlinear Functions
The vertical height, in meters, of a drone above its launch point is modeled by the function , where
and is the time in seconds since liftoff.
Which of the following is the best interpretation of in this context?
For function-interpretation questions, first pin down what the input and output represent, including their units (for example, time in seconds and height in meters). Then rewrite a statement like f(a) = b in words as: when the input is a [units], the output is b [units]. Finally, scan the choices for the one that matches this wording exactly and reject options that talk about rates (per, each second, meters per second) when the function itself only gives a value, not a speed.
Hints
Clarify what each symbol represents
Look at s(t) = 5t^2. What is t measuring, and in what units? What does s(t) represent, and in what units?
Think about s(6) specifically
If s(t) gives the drone’s height at time t, what does plugging in t = 6 tell you? Is s(6) describing a height, a speed, or something else?
Connect your interpretation to the choices
After you compute s(6), ask yourself: which option says that when the time is 6 seconds, the drone’s height is that many meters, without turning it into a speed or a rate like meters per second?
Desmos Guide
Graph the height function
In Desmos, type y = 5x^2. This graph shows the drone’s height y (in meters) as a function of time x (in seconds) after liftoff.
Find the height at 6 seconds
Create a table in Desmos for the equation and include x = 6, or click on the graph at x = 6. Look at the corresponding y-value; this y-value is the drone’s height above its launch point at 6 seconds.
Step-by-step Explanation
Identify input and output of the function
The function is defined as s(t) = 5t^2.
Here, t is the time since liftoff, measured in seconds, and s(t) is the vertical height of the drone above its launch point, measured in meters. So s(t) tells you the drone’s height at time t.
Evaluate s(6) and interpret the numbers
To interpret s(6), plug 6 into the function:
s(6) = 5(6)^2 = 5 · 36 = 180.
So when t = 6 seconds, the value of the function is 180, and the units of s(t) are meters. That means 180 is a height (not a speed or a rate) at the moment t = 6 seconds.
Match the meaning to the answer choices
From the calculation, s(6) = 180 means: at time t = 6 seconds after liftoff, the drone’s height above its launch point is 180 meters.
The only choice that expresses this correctly is: After 6 seconds, the drone is 180 meters above its launch point.