Name:
__________________________________
Date: _________________
Period:
_________
Integrated Advanced Algebra
Notes: Rate of Change Real World Problems
Textbook: Lesson 3.12, Pages 180 – 181
Homework: Worksheet
Essential Question: How can we use average rate of change
to solve real world problems?
Yesterday we learned that we could calculate the average rate of
change between two points by calculating the slope (m) of the line
which passes through the two points:
m
y 2  y1
x2  x1
In real life, average rate of change tells how something changes over
time.
Example 1:
The balance in a savings account over a period of twelve
months is shown in the graph below
The average rate of change of the
savings over the twelve month period can
be found by calculating the slope
between the point representing the
beginning balance in the account (0,
300) and the point representing the
balance in the account after 12 months
(12, 1500)
m
1500  300 1200

 100 dollars / month
12  0
12
Example 2: Using the previous graph, calculate the average rate of
change of the savings account for the following:
a. month 1 to month 4
b.
month 7 to month 8
Name:
__________________________________
Date: _________________
Period:
_________
Note: In a linear function the average rate of change is always
____________________.
Example 3: The distance a marathoner runs over time is represented
by the graph below.
a. What is the average rate of change in
distance over the entire 6 hours of the
race?
b. What is the average rate of change in
distance between the 1st and 2nd hour?
between the 4th and 6th hour?
c. Is the rate of change in distance
constant over the entire 6 hours?
Explain.
d. What is happening between hours 2 and 3?
Explain
Example 4: In 1998, Linda purchased a house for $144,000. In 2009,
the house is worth $245,000. Find the average annual rate of change
in dollars per year in the value of the house. Explain what you
answer means.
Name:
__________________________________
Date: _________________
Period:
_________
Example 5: Kevin’s savings account balance changed from $1450 in
January to $1140 in April. Find the average rate of change per
month. Explain what your answer means.
Name:
__________________________________
Date: _________________
Period:
_________
Integrated Advanced Algebra
Worksheet: Rate of Change Real World Problems
1. The graph below shows the distance a family travels on a trip to the
beach versus the time it takes to get there.
a. What is the average rate of change in
distance over the entire trip?
b. What is the average rate of change in
distance between the 2nd and 4th hour?
between the 4th and 5th hour?
between the 5th and 6th hour?
between the 6th and 8th hour?
c. Are the average rates of change in the above intervals the same?
Explain why or why not.
d. Is the rate of change constant over the entire trip?
2. A golf ball is hit and the height it reaches over time is modeled in the
graph below:
a. What is the average rate of change in height
over the first 2.5 seconds?
between 2.5 sec to 5 sec?
between 0 sec to 1 sec?
between 1 sec to 2 sec?
b. Is the rate of change the same in each
interval? Explain why or why not
Name:
__________________________________
Date: _________________
Period:
_________
c. What is the average rate of change in height over the entire 5
seconds?
3. At 7:00 pm the temperature is 72⁰F. At 10:00 pm it is 52⁰F. Find the
average rate of change in the temperature.
4. In 1990, the value of a prized collector’s coin was $12,500. In 2009,
the value of the coin is $20,050. What is the average annual rate of
change?
5. Pat decides to race the cable car to the top of Stone Mountain. The graph
shows the height, h, at time t above the starting point for Pat and the cable
car.
a. Complete the table for the average rate of change for the given intervals
for Pat and the cable car.
Time
0 – 2 Minutes
2 – 4 Minutes
4 – 5 Minutes
Pat
Cable Car
b. Is the rate of change constant for Pat?
car? Explain
Is it constant for the cable
Name:
__________________________________
Date: _________________
Period:
_________
c. What is Pat’s average rate of change over the entire trip up the
mountain? What is the cable car’s average rate of change over the
entire trip up the mountain?