Chapter 6 worksheet answers

Name Class Date Practice
Form G
Comparing Linear and Exponential Functions
Determine whether each table or rule represents a linear or an exponential
function. Explain.
1.
x
y
1
6
2
10
3
14
4
18
2.
x
y
0
1
2
4
3
144
4
576
4. y = 2 5x
IHSM14_M1_05_03_PRG_TBT_T003
Linear
function; can be written in
y = mx + b form
#
−2
0.25
2
36
#
3. y = 2 5x
IHSM14_M1_05_03_PRG_TBT_T002
Exponential
function; in y = a bx
form
5.
1
9
Exponential function; the y-values have
a common ratio of 6.
Linear function; the y-values have a
common difference of 4.
#
x
y
4
16
Exponential function; the y-values have
a common ratio of 4.
7. y = 6x - 7
IHSM14_M1_05_03_PRG_TBT_T004
Linear
function; in y = mx + b form
6.
x
y
2
37
3
44
4
51
5
58
Linear function; the y-values have a
common difference of 7.
#
8. y = 3 0.7x
IHSM14_M1_05_03_PRG_TBT_T005
Exponential
function; in y = a bx form
#
Can you model the situation by a linear function or an exponential function?
Explain.
9. Kioko’s score increased by 10 points each time she played a video game.
Linear function; increases by a common difference
10. The value of Drew’s car decreases by 6% each year.
Exponential function; decreases by a common ratio
11. The population of a pack of wolves has been increasing annually by 1
8.
Exponential function; increases by a common ratio
12. Each week, Jimi practices his guitar for one hour longer than he did the week before.
Linear function; increases by a common difference
13. Graph the function y = 5x + 3 over the
y
domain 0 … x … 6. Find the average rate
of change over the intervals 0 … x … 2,
180
2 … x … 4, and 4 … x … 6. Describe what you 160
observe.
200
12; 300; 7500; The average rate of change
increases significantly. It is an exponential
function.
140
120
100
80
60
40
20
x
0
1
2
3
4
5
6
7
8
9
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
IHSM14_M1_05_03_PRG_TBT_T001
10
Name Class Date Practice (continued)
Form G
Comparing Linear and Exponential Functions
State whether the equation represents an exponential function, a linear
function, or neither.
#
# x5
14. y = 0.35 2x
exponential function
15. f (x) = 2
neither
16. f (x) = 4 + 8x
linear function
17. y = 0.19x
linear function
18. f (x) = 23
neither
19. f (x) = 0.19x
# x2
exponential function
20. What is the average rate of change for the function g(x) = 4x + 3 over the
intervals 0 … x … 2, 2 … x … 4, and 4 … x … 6? Describe what you observe.
4, 4, 4; The average rate of change is the same over each interval. The rate
of change is constant.
21. What is the average rate of change for the function g(x) = 4
# 3x over the
intervals 0 … x … 2, 2 … x … 4, and 4 … x … 6? Describe what you observe.
16, 144, 1296; The average rate of change is different over each interval. The
rate of change is increasing.
22. Reasoning Ronald wants to invest his summer savings. He has $300 to
invest, and two investments to choose from. For any month t, the balance
of Investment A is given by the function f (t) = 11t + 300, and the balance of
Investment B is given by the function g(t) = 300 1.036t . He built this table
to compare the balances over a period of 8 months.
#
Time (months)
Initial
Balance
1
2
3
4
5
6
7
8
Investment A
(dollars)
300
311
322
333
344
355
366
377
388
Investment B
(dollars)
300
311
322
334
346
358
371
384
398
a. Complete the table of balances to the nearest dollar for Months 3–8.
b. Which investment should Ronald choose and why?
IHSM14_M1_05_03_PRG_TBT_T007
He should choose Investment B because the balance increases exponentially.
The average rate of change for Investment B is increasing, so the balance
eventually overtakes the balance of Investment A, which increases at a
constant rate of $11 per month.
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.