Download UNIT 4B TEST REVIEW: Exponential Functions

 UNIT 4B TEST REVIEW: Exponential Functions
1. In the standard form of an exponential function, 𝑦 = 𝑎 𝑏 ! :
a. What is 𝑎?
b. What is 𝑏?
c. How do you find 𝑏 if you are given the rate (%)?
i. For Growth, 𝑏 is:
ii. For Decay, 𝑏 is:
d. What does x typically represent in word problems?
2.
Wilma and Walder’s Weaving Wanders bought a piece of weaving equipment for $60,000. It is
expected to depreciate at an average of 10% per year.
a) Is this a growth or decay model? ______________________________
b) Write an algebraic equation that models the situation: __________________________
c) Fill in the table’s values for the value of the equipment for the next 4 years. (Round decimals to
the nearest hundredth)
Years
0
1
2
3
4
d) What will the value of the
Value of
equipment be in 10 years?
Equip.
3. The population of termites in Mrs. Woodley’s house is 200. A termite inspector tells Mrs. Woodley that
the number of termites will quadruple every week until she pays for their removal.
a) Is this a growth or decay model? ________________________________
b) Fill in the table values for the expected number of termites for the first 4 weeks. (Round to the
nearest whole number)
c) Write a Next/Now model.
Week
0
1
2
3
4
# of
d) NEXT =
termites
starting at
e) How many termites can Mrs. Woodley expect at the end of 9 weeks?
4.
Miles bought a new boat for $20,000 in 2000. The value of the boat depreciates 8.5% every year.
What would the value of Miles’ boat in 2009? (Let 2000 be year 0.)
5. State the translation that takes place from 𝑓 𝑥 = 3 ! to each of the following.
𝑔 𝑥 = 3! + 8
6.
𝑔 𝑥 = 3 !!! − 5
𝑔 𝑥 = −3 !!! + 1
𝑔 𝑥 = 3 !!!
If the function 𝑓 𝑥 = 4 ! is translated up 6 and left 2, write the new function, 𝑔(𝑥).
7. If the function 𝑓 𝑥 = 1.5 ! is translated down 4 and left 5, write the new function, ℎ(𝑥).
Determine if the function is growth or decay, and then identify the following:
8. 𝑔(𝑥) = 14 0.99
!
9. ℎ(𝑥) = ! !
!
Growth or Decay
Initial:
Growth or Decay
Initial:
Factor:
Rate:
Factor:
Rate:
10. 𝑓 𝑥 =
!
!
8 ! 11. 𝑔(𝑥) = 4 1.34
!
Growth or Decay
Initial:
Growth or Decay
Initial:
Factor:
Rate:
Factor:
Rate:
*Look over your Quiz on Exponents!
12. Rewrite the exponential expression into radical form: 6𝑏
!
!
13. Rewrite the radical expression into exponential form and simplify if needed:
Simplify each exponential expression:
14. !! !
15. 4𝑥 ! 𝑦 !
!! !! ! !
!!
∙ 3𝑦𝑥 !
Simplify each radical expression. Leave in radical form.
16.
81𝑑 ! 𝑜 ! 𝑔!
17.
!
81𝑚 ! 𝑣 ! 𝑝 !
18. Complete the table for the functions and then graph it ON THE SAME PLANE.
y = 6(2)x
x
-3
-2
-1
0
1
2
3
-3
-2
-1
0
1
2
3
y
!
y = 4( )x
!
x
y
!
8𝑚
!
19. Write an exponential function that models the points in the table.
x
y
1
50
2
x
y
Factor:
Initial amount:
1
2
Initial amount:
7.5
Rate (%)
2
8
3
1.125
Now-Next Rule:
4
0.16875
Factor:
Rate (%):
Now-Next Rule:
3
32
4
128
Equation: y=__________
Equation: y=_________
20. Use the table about zombie attacks to answer.
a. Find the exponential regression model. Round to
three decimal places.
15 20 28 38 52 72 96 131 b. What is the correlation coefficient for this data
and what does it tell you? (round to four
decimal places)
c. Using our regression model, determine how
many zombies will be present in 30 minutes.
B A Write the equation of the graph that corresponds
to each equation.
21. 𝑦 = 2
22. 𝑦 =
! !
!
D ! !
C !
23. 𝑦 = 2 !
24. 𝑦 = −2 !
25. 𝑦 = 2𝑥
E Practice Test
b.socrative.com
Class name: PETERS123
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