Name
Algebra 1B
Exponential Word Problems: Solving on Graphing
Calculator
Example 1. A new Mercedes is worth $35,000, but its value decreases by 6.5% each year.
a. Write a function formula for f(t), the dollar value of the Mercedes after t years.
b. Evaluate f(5), and explain what the answer means about the Mercedes.
c. After how many years will the Mercedes be worth $10,000? Find the exact answer. Use a
graph on your graphing calculator.
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Example 2. A car is worth $10,000 when new. Suppose that the car appreciates (increases in
value) by 6% every year.
a. Write a function formula for the car’s value when it is x years old.
b. Find the value of the car when it is 4 years old.
c. When will the car’s value be exactly $16,000?
Find the exact answer. Use a graph on your graphing calculator.
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Name
Algebra 1B
Exponential Regression
You learned how to do linear regression (finding a best-fit line) on your calculator back in the
fall. The steps of exponential regression (finding a best-fit exponential curve) are almost
identical. The only change is choosing the ExpReg command instead of the LinReg command.
Entering the data



Press STAT.
Press ENTER to choose 1:Edit…
You should see two columns labeled L1 and L2. Enter the data in these columns.
Make sure the two columns are of equal length.
Plotting (graphing) the data
 Choose STATPLOT by pressing 2nd Y=.
 Press ENTER to choose 1:Plot1…
 If setting is “Off” change to “On” by pressing ENTER.
 Make sure the next 3 settings are the picture of a scatterplot, L1, and L2. Change if necessary.
 Press GRAPH
 If you can’t see all the points, change the window using ZOOM 9:ZoomStat.
Finding and graphing the best-fit function
 You have to know whether you’re going to use linear regression or exponential regression.
If a problem doesn’t say which to use, make a choice based on the pattern you see in the table
or the shape you see in the plot.
 Enter the data if you haven’t already done so (see “Entering the data” above).
 Press STAT then press  once to see the CALC menu.
 The menu will have choices including 4:LinReg(ax+b) and 0:ExpReg (you’ll need to scroll
down to see ExpReg). Highlight the one you want and press ENTER.
 Press ENTER once or twice, as needed to get the calculator to display the answer, an
equation for the best-fit function of the type you requested. (It will show the general form
and two numbers a and b; you have to put in those numbers in place of letters in the general
form.)
 To graph this line on the same screen as the data, start on a blank line on the Y= screen,
then type the equation you just found.
 Press Graph to see the curve
Resetting your calculator when you’re finished
 Choose STATPLOT (2nd Y=) then highlight 4: PlotsOff and hit ENTER twice.
Example: Suppose that census counts of Midwest wolves began in 1990 and produced these
estimates for several different years.
0
2
5
7
10
13
Years since 1990
100
300
500
900
1,500
3,100
Estimated Wolf
Population
Write an exponential function that most closely represents the data above using exponential
regression on your calculator.
y=
Use your function formula to estimate the wolf population in 1993.
Name
Algebra 1B
Name
Algebra 1B
1. Hypothermia is a life-threatening condition in which body temperature falls well below the
norm of 98.6F. However, because chilling slows normal body functions, doctors are exploring
ways to use hypothermia as a technique for extending time of delicate operations like brain
surgery.1
The following table gives experimental data illustrating the relationship between body
temperature and brain activity.
body temperature (F)
brain activity (% of normal)
50
11
59
16
68
24
77
37
86
52
98.6
100
a) Use exponential regression on your calculator, find a y = ··· rule that models the
table.
y=
b) Estimate the level of brain activity at a body temperature of 39F (the lowest
temperature that’s been used in surgery experiments on animals).
c) Sketch a picture of the scatter plot and the exponential function from part a.
USA Today, August 1, 2001, “Surgery’s Chilling Future Will Put Fragile Lives on Ice.” per citation in Core-Plus
Mathematics: Contemporary Mathematics in Context, Course 1, page 357.
1
Name
Algebra 1B
2. Mr. Noguita cleaned out his attic, and put a “Free Books” pile on the curb in front of his
house.
After t hours, the number of books remaining on the table was given by the function
B(t) = 200 · (0.89)t.
a. Describe how the number of books in the pile is changing each hour.
The answer should involve a percent of increase or decrease.
b. How many books are there after 10 hours?
c. How many hours until there are 100 books? Find an exact answer. Use a graph on your
calculator.
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Name
Algebra 1B
3. A classroom has a supply of 200 pencils at the start of the school year. Each month, 12.5% of
the pencil supply is used up or lost.
a. Complete this table showing the number of pencils after each month.
month number
0
1
number of pencils
200
2
3
4
5
b. Write a function formula showing the number of pencils after x months.
c. The teacher wants to order more pencils when there are exactly 20 pencils remaining.
After how many months will this happen? Find an exact answer. Use the graph on your
graphing calculator.
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Name
Algebra 1B
4. Here is a table showing the price of a car as a function of its age.
Let P(t) stand for the price of the car after t years.
t (age in years)
0
1
2
3
4
P(t) (price in dollars)
$20,000
$18,000
$16,200
$14,580
$13,122
a. What number do you multiply to go down the table.
b. Write a function formula.
c. What is the percent rate of decrease each year?
d. After how many years will the car be worth $5,000? Find an exact answer. Use a graph
on your graphing calculator.
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