A leaf hangs from a branch 12 feet in the air. It falls to the ground at a rate of 0 point 2 5 feet per second. Which graph could represent the leaf’s height in feet as a function of time, in seconds, after leaving the branch?
Answer
A
Image with description A coordinate plane showing Falling Leaf, Time in seconds on the x-axis and Height in feet on the y-axis. A line is passing through (0, 16), (6, 8), and (12, 0).
B
Image with description A coordinate plane showing Falling Leaf, Time in seconds on the x-axis and Height in feet on the y-axis. A line is passing through (4, 20 ), (6, 14), and (12, 0).
C
Image with description A coordinate plane showing Falling Leaf, Time in seconds on the x-axis and Height in feet on the y-axis. A line is passing through (0, 12), (8, 8), and (20, 2).
D
Image with description A coordinate plane showing Falling Leaf, Time in seconds on the x-axis and Height in feet on the y-axis. A line is passing through (0, 12), (8, 10), and (16, 8).
Explanation
The leaf starts at 12 feet, so its graph must pass through (0, 12). It falls 0.25 feet each second, giving the height rule h = 12 − 0.25t. After 8 seconds its height is 10 feet, and after 16 seconds it is 8 feet; choice D shows these points.
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