MODULE
STUDY GUIDE REVIEW
15
Exponential Equations
and Models
Essential Question: How can you use exponential equations to
represent real-world situations?
Key Vocabulary
exponential decay
(decremento exponencial)
exponential growth
(crecimiento exponencial)
exponential regression
(regresión exponencial)
(Lesson 15.2)
KEY EXAMPLE
A comic book is sold for $3, and its value increases by 6% each
year after it is sold. Write an exponential growth function to find
the value of the comic book in 25 years. Then graph it and state its
domain and range. What does the y-intercept represent?
Write the exponential growth function for this situation.
y = a(1 + r)
t
= 3(1 + 0.06)
= 3(1.06)
t
t
Find the value in 25 years.
y = 3(1.06)
t
= 3(1.06)
25
≈ 12.88
After 25 years, the comic book will be worth approximately $12.88.
(t, y)
t
y
0
3
(0, 3)
5
4.01
(5, 4.01)
10
5.37
(10, 5.37)
15
7.19
(15, 7.19)
20
9.62
(20, 9.62)
25
12.88
(25,12.88)
30
17.23
(30, 17.23)
y
16
Cost ($)
© Houghton Mifflin Harcourt Publishing Company
Create a table of values to graph the function.
12
8
4
t
0
10
20
30
Time (years)
The domain is the set of real numbers t such that t ≥ 0.
The range is the set of real numbers y such that y ≥ 3.
The y-intercept is the value of y when t = 0, which is the time when the comic book was sold.
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EXERCISES
Solve each equation for x. (Lesson 15.1)
5 = 25
___
x
1.
3(2) = 96
3.
The value of a textbook is $120 and decreases at a rate of 12% per year. Write a function to model the
situation, and then find the value of the textbook after 9 years. (Lesson 15.2)
x
2.
25
Find an exponential model for the data in the given table. (Lesson 15.3)
4.
x
0
1
2
3
4
5
6
7
8
9
10
y
9
12.85
16.89
28.15
42.58
65.1
99.34
153
237.6
339.2
478.61
State whether each situation is best represented by an exponential or linear function. Then write
an exponential or linear function for the model and state whether the model is increasing or
decreasing. (Lesson 15.4)
5.
A customer borrows $950 at 6% interest compounded annually.
6.
The population of a town is 8548 people and decreases by 90 people each year.
MODULE PERFORMANCE TASK
Half-Life
The half-life of iodine-131 is 8 days, and the half-life of cesium-137 is 30 years. Both of these
isotopes can be released into the environment during a nuclear accident.
© Houghton Mifflin Harcourt Publishing Company
Suppose that a nuclear reactor accident released 100 grams of cesium-137 and an unknown
amount of iodine-131. After 40 days the amount of iodine-131 is equal to the amount of
cesium-137. About how much iodine-131 was released by the accident?
Start by listing in the space below how you plan to tackle the problem. Then use your own
paper to complete the task. Be sure to write down all your data and assumptions. Then use
numbers, graphs, tables, or algebra to explain how you reached your conclusion.
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Study Guide Review
Ready to Go On?
15.1–15.4 Exponential Equations
and Models
• Online Homework
• Hints and Help
• Extra Practice
1.
Mike has a savings account with the bank. The bank pays him annual interest of 1.5%. He has $4000
and wonders how much he will have in the account in 5 years. Write an exponential function to model
the situation and then find how much he will have. (Lesson 15.1)
State each function’s domain, range, and end behavior. (Lesson 15.2)
2.
ƒ(x) = 900(0.65)
4.
The table shows the temperature of a pizza over three-minute intervals after it is removed from
the oven.
x
Time, (x)
Temperature, (y)
3.
ƒ(x) = 400(1.23)
0
4
8
12
16
450
340
240
190
145
x
© Houghton Mifflin Harcourt Publishing Company
Create a model describing the data and use it to predict the temperature after 20 minutes.
(Lesson 15.3)
5.
Account A and B each start out with $600. If Account A earns $50 each year and Account B earns
6% of its value each year, after how many years will Account B have more money than Account A?
(Lesson 15.4)
ESSENTIAL QUESTION
6.
Module 15
How can you identify an exponential equation?
765
Study Guide Review
MODULE 15
MIXED REVIEW
Assessment Readiness
1. Consider the end behavior of f(x) = 75(1.25) . Select True or False for each statement.
A. As x → -∞, y → -∞.
True
False
B. As x → -∞, y → 0.
True
False
C. As x → ∞, y → ∞.
True
False
x
2. An engineer took the following measurements: 3.22 cm, 14.1 cm, 18 cm,
and 24.025 cm. Choose True or False for each statement.
A. The most precise measurement has
4 significant digits.
True
False
B. Written using the correct number of
significant digits, the sum of the
measurements should be rounded to
the ones place.
True
False
C. The least precise measurement has
2 significant digits.
True
False
3. Solve 36(3) = 4. What is the value of x? Explain how you got your answer.
x
4. Consider the following situation: enrollment at a school is initially 322 students and
grows by 4% per year. Write an equation to represent this situation, and use it to predict
the number of students at the school in 5 years.
© Houghton Mifflin Harcourt Publishing Company
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Study Guide Review