February 06, 2015
Aim: To calculate average rate of change
Homework: Worksheet (posted on website)
Warm Up: Calculate the rate of change of each of the following lines.
1)
2)
February 06, 2015
In most cases, it is not realistic to travel at a constant speed for an entire trip. In
these cases, however, it is possible to calculate the average speed that was
traveled between specific time intervals...
(60,27)
In this graph, Sascha recorded her
distance traveled at five different points
during her bike ride. The results are
labeled on the graph.
(44,23)
(15,10)
(7,8)
* Since each line segment has a different
slope, this shows that she traveled at
different speeds throughout her trip.
However, we can represent what her
average speed (slope) was by creating an
imaginary line segment from the start of
her trip to the end of her trip.
(0,0)
Using this created line, we can calculate
what is called her "average rate of
change".
February 06, 2015
Average Rate of Change: the slope of an "imaginary" line between two
specified points in a function.
* Calculating "average rate of change" is the same as calculating slope.
Ex 1: Consider the function f(x) = x2 + 3. Find its average rate of change in the
interval -1 ≤ x ≤ 3.
February 06, 2015
Ex 2: (You Try)
The function h(x) is given in the table below. Which of the following choices
shows the average rate of change of the function over the interval 2 ≤ x ≤ 6?
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1 Assessment Question!
A
B
C
D
February 06, 2015
Application:
A: Frank is selling lemonade. The function
models the number of
glasses he sold, g(t), after t hours. What is the average rate of change between hour 2
and hour 6? Show all work.
B: The table shows the average diameter of a person's pupil as a
person ages. What is the average rate of change of a person's
average pupil diameter from age 30 to 70? Be sure to include
units.
C: 25 beetles are left in a bin, undisturbed, for 5 weeks. Each
week, the number of beetles is recorded. The equation P(x) =
25•2x models the number of beetles, P(x), after x weeks.
1) Calculate the average rate of change between Weeks 1 & 3
2) Calculate the average rate of change between Weeks 0 & 5
3) Between which pair of weeks, 1-3 or 0-5, is the average
rate of change greatest? Why do you think this is the case?
Construct the graph and the equation of a non-linear function that has
an average rate of change equal to 2 within the interval 0 ≤ x ≤ 3.
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Summary: Exit Slip
Given the function f(x) = 2x2 - 4, find the average rate of change within the
interval 0 ≤ x ≤ 3.