Name: _____________________________ Period: _____________
Date: ______________
Chapter #7: Exponentials Functions Review Sheet
Write the formula for Questions #1-7.
1. Arithmetic Sequence
2. Geometric Sequence
3. Common Difference
4. Common Ratio
5. Exponential Decay
6. Exponential Growth
7. Compound Interest
Answer all of the following. Show all work for the following problems including all necessary formulas
and substitutions.
8. Find the next term of the sequence 2, -10, 50, …
10. If 𝑓(𝑥) = 5(3)𝑥 , find the value of f (2).
12. The expression (22 )(25 ) is equivalent to
(1) 27
(3) 47
(2) 210
(4) 410
9. Which expression is equivalent to (2x2)3?
11. The expression
(10𝑤 2 )
5𝑤
3
is equivalent to
13. Which expression is equivalent to x-2?
(1)
1
𝑥2
(2) -2x
(3) x2
(4)
1
𝑥 −2
2
14. If the first term of a geometric sequence is 3
and the common ratio is 3, find the 7th term.
16. The table below shows the average yearly
balance in a savings computations account where
interest is compounded annually. No money is
deposited or withdrawn after the initial amount is
deposited.
15. What is the value of 20 + 2-2?
17. A population that initially has 20 birds
approximately doubles every 10 years. Which graph
represents this population growth?
Which type of function best models the given data?
(1) linear function with a negative rate of change
(2) linear function with a positive rate of change
(3) exponential decay function
(4) exponential growth function
18. The table below represents the function F.
x
y
-1
2
0
3
1
4.5
2
6.75
3
10.125
The equation that represents this function is
(1) F(x) = 3(1.5)x
(2) F(x) = 1.5x
(3) F(x) = (1.5)x + 3
(4) F(x) = 2x + 3.275
19. Which of the following graphs represent
exponential decay?
(1)
(2)
(3)
(4)
Answer all parts to each of the following. Partial credit is awarded.
21. The function f(t) = 100(1.05)t models the growth
of a fruit fly population, where f(t) is the number of
flies and t is time in days. In the function f (t),
explain what 1.05 and 100 represent.
20. Kristen invests $5,000 in a bank. The bank pays
6% interest compounded monthly. Write an
equation that can be used to find A, her account
balance after t years.
Show all work for the following. Partial credit is awarded. Be sure to show all formulas and substitutions
necessary for full credit.
22. A cup of soup is left on a countertop to cool. The table below gives the temperatures, in degrees Fahrenheit,
of the soup recorded over a 10-minute period.
Time in
Minutes
Temperature
in oF
0
2
4
6
8
10
180.2
165.8
146.3
135.4
127.7
110.5
a. Write an exponential regression equation for the
data, rounding all values to the nearest hundredth.
b. Using your equation from part a, predict the
temperature of the soup after 15 minutes. Round to
the nearest tenth.
23. Solve the system graphically:
y = 5(3)x
y = -2x + 5
24. In 2000, 2200 students attended Polaris High School. The enrollment has been declining 2% annually.
a. Write an equation for the enrollment of Polaris High School t years after 2000.
b. If this trend continues, how many students will be enrolled in 2015?