Co n cep t Byt e
Use Wit h Lesson 9-2Rates of Increase
Co m m o n Co r e St a t e St a n d a r d s
F-LE.A.3 Observe using graphs and tables that a
quantity increasing exponentially eventually exceeds
a quantity increasing linearly, quadratically, or (more
generally) as a polynomial function. A ls o F-IF.B.6
MP 8In this activity, you will use functions, tables, and graphs to determine and compare
rates of change presented in various forms.Activity 1
The function h(t) = 201 - 512 represents the approximate height of a ball
that is thrown upward with an initial velocity of 20 m /s, where h{t) is the height
(in meters) of the ball after t se co n d s.- Graph the function on a graphing calculator.
- Copy and complete the tables.
1
2
3
4mm m ■ TijR filTOM
0 s to 1 s
1 s to 2 s
2 s to 3 s
3 s to 4 s- Does the average rate of change increase or decrease from 0 s to 2 s? Justify your
answer using your graph. - Does the average rate of change increase or decrease from 2 s to 4 s? Justify your
answer using your graph. - M ak e a conjecture What do the positive and negative signs of the average rate of
change indicate? Use the scenario and the graph to check your conjecture.
M1Ex e r c i se s
A toy car is traveling up an inclined plane. The graph shows the distance the car has
traveled at t seconds. Use the graph to answer Exercises 6-9.- Estimate the distance the car has traveled at 1 second, at 3 seconds, and at 5 seconds.
- What is the average rate of change from 1 s to 3 s?
- What is the average rate of change from 3 s to 5 s?
- Does the average rate of change increase or decrease? Explain how the graph can
help you answer this question.
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