Exponential Functions Review Sheet
Graph each of the following.
1. y = 3x
2. y = (1/4)x
3. y = (2/3)x
4. What is the equation of the reflection of y = 6x in the y-axis?
5. What is the equation of the reflection of y = 3x in the x-axis?
Solve each of the following for x.
6. 4x+2 = 43
7. 5x-1 = 125
8. 8x = 4x+1
9. 1000x = 100x-1
10. 272x+4 = 9x
11. 32x-1 = 27
12. (1/16)x-1 = 82-x
13. 362x-10 = (1/36)x-5
14. 3𝑥
15. 3x = (1/9)
16. 73x = 495-x
17. 252x-10 = 1253x
2 -3x
= 81
Word Problems.
18. $2000 is deposited into an account that earns 6% annual interest, compounded monthly. Find
the balance after 10 years.
19. How much would you deposit in an account that pays 8% interest, compounded monthly to
have a balance of $1000 after 10 years (to the nearest dollar)?
20. A principle of $800 is deposited in an account that pays 7.2% interest, compounded
quarterly. Find the balance after 8 years.
21. You deposit $10,000 in an account that pays 6% interest. Find the balance after 10 years if
the interest is compounded continuously.
22. $1250 is deposited in an account that pays 6.5% annual interest, compounded continuously.
What is the balance after 8 years?
23. You have inherited a house that was purchased for $20,000 in 1950. It is now 2010, and the
value of the house increased by approximately 5% each year. What is the value of the house
now?
24. Your collection of baseball cards cost you $150 in 1988. The value of the collection had
increased by 7.5% each year. What is the value of the cards in 2012?
25. You have inherited an emerald ring that had an appraised value of $2400 in 1960. It is now
2010 and the appraised value of the ring has increased by 6% each year. What is the value now?
26. In 1980, the population of Shady Bridge was 2500. Each year the population increased by
1.8%. Write an equation to model this population. Form the equation, what would the population
have been in 1996?
27. 100 grams of radioactive actinium decays according to the model A = 11(2)-0.05t where A is
the amount(in grams) and t is the time(in years). Find the amount remaining after 5 years (to the
nearest tenth).
28. In 1980, the population of a town was 12,000. If the population increases by 4% each year,
what would the population have been in 1995?
29. A 70,000-gallon swimming pool is leaking water at the rate of 10% per week. Write an
equation to model the volume of water in the pool after t weeks. Use the equation to determine
how much water will remain after 4 weeks.
30. The relationship between air pressure (P) and altitude (h) can be modeled by P = 14.7e-.00004h.
Mount Everest rises to a height of 29,108 feet above sea level. What is the air pressure at the
peak of Mount Everest (to the nearest tenth)?
31. One hundred grams of radium is stored in a container. The amount of radium, R (in grams),
present after t years is given by R = 100e-.00043t. How much of the radium will remain after
10,000 years (to the nearest hundredth)?
Answer Key:
1. x y
-3 .04
-2 .11
-1 .33
0 1
1 2
2 9
4. y = (1/6)x
5. y = -3x
6. x = 1
7. x = 4
8. x = 2
9. x = -2
10. x = -3
11. x = 2
12. x = -2
13. x = 5
14. x = 4, -1
15. x = -2
2. x
-1
0
1
2
3
4
y
4
1
.25
.06
.015
.003
16. x = 2
28. 21,612 people
17. x = -4
29. 45,927 gallons
18. $3638.79
30. 4.6
19. $451
31. 1.36 grams
20. $1415.86
21. $18,221.19
22. $2102.53
23. $373,583.72
24. $850.93
25. $44,208.37
26. y = 2500(1 + .018)x and 3326 people
27. 9.2 grams
3. x
-5
-4
-3
-2
-1
0
1
2
y
7.6
5.1
3.4
2.25
1.5
1
.67
.44