Name:
Date: ________________
Algebra 1B
Exponents and Exponential Functions
More Review Problems
1. Evaluate without using a calculator. Show your steps.
a. 01 + 13 + 2–1 + 3–2 + 40
Hint: Order of operations. First do exponents.
b. ( 43 )–3

c. 2–5 (24)
10 4
d.
10 8

2. Rewrite each of the following as a power of x. Negative exponents okay. Show your steps.
a. x 4  x 1 


(x 3 ) 3
b.
(x 5 ) 2
4
 1 
c.
x 2 

d.

x 2
x 2
1
x2
Algebra 1B
Exponents and Exponential Functions
3. Simplify as much as possible. Show steps. Final answers should not have negative exponents.
a. (–2c)6
n
5
7
n
b.

c. (3xy2)4 

d.

3
 k 1
k
n2
5
e.
a 
b 
f.
 2x 
 2 3 
x y 


x
y
3
Algebra 1B
Exponents and Exponential Functions
4. Answer these questions about the function f(x) = 1.3 · (0.2)x.
a. Is this percent increase or percent decrease function? Explain how you can tell just by
looking at the formula.
b. Suppose this function formula came from a word problem involving a percent increase or
decrease. What would the percentage be?
c. Which of these is the shape of the graph of f(x)?
5. Sketch the graph of f(x) = 1.3 · (0.2)x below.
Be sure to label to y-intercept.
6. Determine whether each of these situations is linear or exponential.
If it’s linear, identify the rate (the slope), and write: linear, m = ···
If it’s exponential, identify the multiplier (base), and write: exponential, b = ···
a. increasing by 37% each year
b. increasing at a steady rate of 37 per year
c. decreasing by 37% each year
d. decreasing at a steady rate of 37 per year
e. each year, having 37 times as much as in the previous year
f. each year, keeping 37% of the previous year’s amount
Algebra 1B
Exponents and Exponential Functions
7. For each table below, there is either a linear function or an exponential function that fits the
table exactly. Find the y = ··· equation.
a.
x
y
0
500
Exponential
1
460
or
2
420
3
380
Linear
4
340
5
300
6
260
7
220
y = __________________.
b.
x
y
0
640
Exponential
1
320
or
2
160
3
80
Linear
4
40
5
20
6
10
7
5
y = __________________.
c.
x
y
0
40
1
47.5
2
55
Exponential
or
Linear
x
y
1
3
2
4.5
or
Linear
3
62.5
4
70
5
77.5
6
85
7
92.5
y = __________________.
d.
0
2
Exponential
3
6.75
4
5
6
7
10.125 15.1875 22.78125 34.171875
y = __________________.
8. Write two words describing each of these graphs. One of the words should be either
linear or exponential. The other should be either growth (increase) or decay (decrease).
Algebra 1B
Exponents and Exponential Functions
9. For each of these problem situations, decide if it is linear or exponential and write a y = ···
equation.
a. When Emma was in Kindergarten (think of Kindergarten as “Grade 0”), her parents gave
her a weekly allowance of $1.00. Each time she moved up a grade, this allowance was
increased by $0.50. Write an equation for finding Emma’s allowance in Grade x.
Exponential
or
Linear
y = __________________.
b. In year 2000, the ticket price at a movie theater was $7.50. Each year since, the price has
increased by 5%. Write equations for finding the ticket price, where x stands for the
number of years since year 2000.
Exponential
or
Linear
y = __________________.
c. An investor bought $10,000 of stock in a company that turned out to not do very well.
Each year, the investment’s value decreased by 7%. Write equations for finding the value
of the investment after x years.
Exponential
or
Linear
y = __________________.
d. Joe has a big pile of laundry to wash. There are 140 pieces of clothing to be washed.
He can wash 20 pieces in each laundry load. Write equations for finding how many
clothes are left after doing x loads of laundry.
Exponential
or
Linear
y = __________________.
e. 200 students signed up to be members of a club, but only 90% of them actually came to
the first meeting, and the attendance at each subsequent meeting was 90% of the
attendance at the meeting before. Write equations for finding the attendance at meeting
number x of the club.
Exponential
or
Linear
y = __________________.
Algebra 1B
Exponents and Exponential Functions
ANSWERS
1.
a. 0 + 1 + ½ + 1/9 + 1 = 1/9 + 5/2 = 2/18 + 45/18 = 47/18
b. 64/27
c. ½
d. 1/10,000
2.
a. x
c. x-8
b. x-1
d. x 0 =1
3.
a. 64c6
c. 81x5y7
e. b5/a5

b. n2/35
d. 3n2/k2
f. -8/x3y9
4.
a. decrease – base (.2) is less than one
b. 80%
c. 4th graph
5.
1.3 ---
6.
a. exponential 1.37
c. exponential .63
e. exponential 37
b. linear 37
d. linear -37
f. exponential .37 (don’t worry if this one was tricky)
7.
a. linear y = -40x + 500
c. linear y = 7.5x + 40
b. exponential y = 640 * .5x
d. exponential y = 2 * 1.5x
8.
linear growth exponential growth
linear decay
exponential decay
9.
a. linear y =.5x + 1
b. exponential y = 7.5 * 1.05x
c. exponential y =10,000 * .93x
d. linear y = -20x + 140
e. exponential y = 200 * .90x (don’t worry if this one was tricky)