NAME: ___________________________ Date: __________
PERIOD: _______
Exponential Functions and Comparing Functions Review: Units 4 – 5
Constructed Reponse. SHOW ALL YOUR WORK
1)
2) The population of Whoville is increasing at a rate of 13% each year since 2012. The
population in 2012 was 22,000 people.
a. Write an equation to determine the population of Whoville, x years since 2012.
b. What will be the population of Whoville in 2017?
c. If the trend continues, when will the population exceed 70,000?
3) A car depreciates at a rate of 8% each year. The car was bought for $32,000. How
much will the car be valued in 7 years?
4) Write the equation of the graph below.
NAME: ___________________________ Date: __________
PERIOD: _______
5) The function y = 2x is stretched vertically by a factor of 5, shifted left 3 units and down
8 units. Write the new equation.
6)
a) Write the explicit rule for the sequence above.
b) Write the recursive rule for the sequence above.
7)
Use the graph to:
a) State the domain
b) State the range
c) State the Asymptote
d) End behavior: as x increases, f(x) _____
as x decreases, f(x) _____
e) ARC of 0 < x < 3
8)
Write the equation represented in the table.
NAME: ___________________________ Date: __________
PERIOD: _______
9) Given the sequence 7, 10, 13, 16, . . .
a. Does it appear to be linear or exponential?
b. Determine an explicit function to describe the sequence.
c. What would the 20th term of the sequence be?
10)
a. Which function has the greater average
rate of change from [0, 2]?
b. Over what interval is f(x) > g(x)?
c. Over what interval is g(x) > f(x) ?
11) Write the equation of the function in the table:
x
2
4
6
f(x)
3
7
11
12) The student council makes an initial investment in a savings account that earns
interest. The value of the savings account after m months is determined by the function
v(m) = 2,000(1.005)m. The student council also has a checking account which has a
value after m months that is determined by the function c(m) = 250 + 100m.
A: What is the initial investment in the savings account?
B: What is the interest rate of the savings account?
NAME: ___________________________ Date: __________
PERIOD: _______
C: When the student council has $2,450 in its checking account, it will purchase new
computers for the library.
After how many months will the student council purchase new computers
for the library?
Multiple Choice
13) What transformation would make f(x) < g(x) for all values of x?
a) –f(x)
b) f(x – 2)
c) f(x) + 3
d) f(x) - 2
14)
15) Write the explicit rule for the sequence: -8, -2, -1/2, …
A. an = -8(2)n – 1
1
B. an = -4(8)n – 1
1
C. an = -2(4)n – 1
1
D. an = -8(4)n – 1
1
4
16) The recursive rule for a geometric is given as an = an – 1(− ) with a1= 256. What are
the first four terms of the sequence?
A. -1/4, 1, -4, 16
B. 256, -64, 16, -4
17) Write the equation of the graph below:
C. 256, 64, 16, 4
D. -256, 64, -16, 4
NAME: ___________________________ Date: __________
PERIOD: _______
18) The exponential function above has been transformed to:
g(x) =-(3)x+3 – 7
Describe the transformation that occurred.
A. Reflected across x axis, left 7, up 3
B. Reflected across x axis, left 3, down 7
C. Vertical stretch by 3, left 3, up 7
D. Left 3, down 7
19) What is the solution to the exponential equation?
9x = 812x – 12
A. x = 8
B. x = -24
C. x =12
D. x = 3
20) Which data set below represents an EXPONENTIAL model?
A {(2, 4), (3, 3), (4, 2), (5, 1)}
B {(0, 16), (1, 4), (2, 1), (3, ¼)}
C {(0, 5), (1, 6), (2, 9), (3, 14)}
D {(1, 4), (2, 8), (3, 12), (4, 16)}
21) Which function is an ODD function?
a. y = 2x2 + x
b. y = 3x3+ 2x
c. y = 4x2 – 1
d. y = x5 – x2 + 6x
22) Which of the following data sets is best described by a QUADRATIC model?
A {(1, -2), (2, -4), (3, -6), (4, -8)}
B {(1, 2), (2, 4), (3, 6), (4, 8)}
C {(1, -1), (2, 2), (3, -4), (4, 8)}
D {(1, -1), (2, 2), (3, 7), (4, 14)}
23) Argyle has $1000 in his savings account.
He wants to save more money. He is looking at two investment plans. Under plan A, he will
increase his account balance by $200 a year. Under plan B, he will increase his account
balance by 15% each year. How much more will he save with Plan B after 10 years?
A $1,046
B $131
C $459
D $11