Algebra
Chapter 7 Review
1. Eight years ago, Rudi thought that he was making a sound investment by buying $1000 worth of Pro Sports
Management stock. Unfortunately, his investment depreciated steadily, losing 15% of its value each year. How
much is the stock worth now? Write an equation and solve for the answer.
2. A scientist left a 32-gram sample of a radioactive substance out and it was exposed to the air. After 30
minutes, only 26 grams remained.
a.
How much was left when the janitor found it 8 hours after the scientist left?
b.
When will there be only 1 gram of the substance?
3. Find an equation for the exponential growth of population in the U.S. if in 1970 the population was 203
million and ten years later, 1980, the population was 226 million. (So, t(0) = 203 and t(10) = 226.)
4. Aaron just inherited $8000 from his grandmother. He plans to invest the money, not touching it for twenty
years. He can invest in treasury bills at 6.67% interest, compounded annually, or in a money market account
earning 6.5% annual interest, compounded weekly. Which should he do? Justify your answer.
5. Each table below represents an exponential function of the form y  ab x . Complete each table and find the
corresponding rule.
a.
b.
x
y
x
y
0
3.1
0
3
1
4.34
1
2 6.076
2
108
3
3
4
4
c.
d.
x
0
1
2
6.
7.
3
y
4
40
5
32
6
25.6
Totals
$21
$15
$12
$10
30
x
0
1
2
3
y
1600
2000
2500
3125
Is y = 3(1)x an exponential function? Explain why or why not.
Write an equation that represents the function in this table.
Week Weight of Bacterial
Culture (g)
1
756.00
2
793.80
3
833.49
8. Elmer loves rabbits! He started with 150 rabbits, but the number keeps doubling every year. How many
rabbits will Elmer have after five years?
9. Find the annual growth rate (interest rate) on an account that was worth $150 in 1972 and $540.53 in 1994.
10. Antonio is president of Maths-R-Us and has asked his financial advisor for a report about the company’s
expected profits. The advisor told him that the profits were expected to follow the equation y = 150210(0.82)x
over the next 12 months. Tell Antonio everything you can tell about the company from the equation.
11. In seven years, Seta’s son Stu is leaving home for college. Seta hopes to save $8000 to pay for his first year.
She has $5000 now and has found a bank that pays 7.75% interest, compounded daily. At this rate, will she
have the money she needs for Stu’s first year of college? If not, how much more does she need?
12. Molly and Tess like to shop at the mall. Their sister Jessica prefers to play bocce ball instead. Molly has
$280 in her bank account and spends $40 every trip. Tess has $170 in her account and spends half as much as
Molly during each trip. Jessica has $50 in her account and does not spend any of it. Find the number of trips it
will take for the Molly and Tess to have the same amount of money in their accounts.
13. Two car-rental agencies are competing for business. Mertz charges $35 a day and $0.15 per mile, and
Mavis charges $20 a day and $0.45 per mile.
a. Write an equation that represents the charges to rent a car at each agency.
b. Find the point of intersection and explain what it means.
c. Which agency should you choose? Why?
14. Fredrico’s Bank will let you decide how often your interest will be computed, but with certain restrictions.
If your interest is compounded yearly you earn 8%. If your interest is compounded quarterly, you earn 7.875%.
Monthly compounding yields a 7.75% interest rate, while weekly compounding yields a 7.625% interest rate. If
interest is compounded daily, you ear 7.5%. If you start with 100, how much money will you have under each
of the conditions above?
15. At the Pico de Gallo Restaurante, the dinner specials include combinations of tacos and enchiladas. The
Number One special offers 2 tacos and 3 enchiladas for $8.00. The Number Two special offers 3 tacos and 1
enchilada for $7.45.
a. Let t equal the cost of one taco and e equal the cost of one enchilada. Write two equations, one to
show the cost of the Number One special, and another to show the cost of the Number Two special.
b. Find the cost of each enchilada and taco. Show all your work.
16. Write the multiplier for each condition:
a.
b.
c.
d.
e.
f.
g.
h.
earning 6.5% interest
depreciating 35% annually
3% interest compounded quarterly
decreasing at a rate of 19% per year
5.75% interest compounded bi-annually (every six months)
decaying at a rate of 26% each day
increasing by 1.93%
7% compounded monthly
17. Rewrite each expression in radical form.
a.
16
5
4
b.
(−8)
2
3
c.
2
3
(64)
d.
1
3
(−27)
18. Write an equation for an exponential function that passes through each pair of points:
1
a. (0, 8) and (4, 2 )
d. (–1, 72.73) and (3, 106.48)
b. (0, 60 and (3, 48)
c. (1, 21) and (2, 147)
e. (–2, 351.5625) and (3, 115.2)
19. Review all rules of exponents!
Answers:
1. 𝒚 = 𝟏𝟎𝟎𝟎(𝟎. 𝟖𝟓)𝒙 ; his stock is now worth $272.49.
2. [ a: ≈ 1.15 grams b: ≈ ]
3. [ P(n) = 203(1.0108)n ]
4. [ The money market account will yield a little more. ]
c: 𝒚 = 𝟓𝟎(𝟎. 𝟖)𝒙
5. [ a: y  3.1(1.4)x , b: y  3  6x
6.[ No, it is linear. ]
d. 𝒚 = 𝟏𝟔𝟎𝟎(𝟏. 𝟐𝟓)𝒙
7. [ 𝒚 = 𝟕𝟐𝟎(𝟏. 𝟎𝟓)𝒙 ]
8. [ 4800 ]
9. [ ≈ 6%]
10. [ Sample statements: They begin with $150,210.00 expected profit, which is decreasing at a
rate of 18% per month. At the end of the year, they will have $13,882.42 expected profit. ]
11. [ Yes, she will have about $9601.02 by then. The daily rate is
2555 days, so we use the equation: = $𝟓𝟎𝟎𝟎(𝟏. 𝟎𝟎𝟎𝟐𝟏𝟐𝟑𝟐𝟗)
𝟎.𝟎𝟕𝟕𝟓
𝟐𝟓𝟓𝟓
𝟑𝟔𝟓
≈ 𝟎. 𝟎𝟎𝟎𝟐𝟏𝟐𝟑𝟐𝟗. Seven years is
≈ $𝟖𝟔𝟎𝟏. 𝟎𝟐 ]
12. [ 5.5 (or 6) trips]
13. [ a: y  0.15x  35 , y  0.45x  20 , b: (50, 42.5) means that both cars cost $42.50 at the 50-mile mark,
c: If you drive less than 50 miles, you should choose Mavis, and if you drive more than 50 miles, you
should choose Mertz. ]
14. Starting with $100, after one year you will have $108 if compounded annually; $108.11 compounded
quarterly; $108.03 compounded monthly; and $107.79 compounded daily.
15.[ a: 2t + 3e = 8, 3t + 1e = 7.45; b: one taco = $2.05, one enchilada = $1.30 ]
16. [ a. 1.065; b. 0.65; c. 1.0075; d. 0.81; e. 1.02875; f. 0.74; g. 1.0193; h. ≈ 1.00583 ]
𝟒
17. [ a. ( √𝟏𝟔)𝟓 = 𝟑𝟐
𝟏
𝟑
𝟑
𝟑
; b. ( √−𝟖)𝟐 = 𝟒 ; c. ( √𝟔𝟒)𝟐 = 𝟏𝟔 ; d. √−𝟐𝟕 = −𝟑
18. [ a. 𝒚 = 𝟖(𝟐)𝒙 ; b. 𝒚 = 𝟔(𝟐)𝒙 ; c. 𝒚 = 𝟑(𝟕)𝒙 ; d. 𝒚 = 𝟖𝟎(𝟏. 𝟏)𝒙; e. 𝒚 = 𝟐𝟐𝟓(𝟎. 𝟖)𝒙 ]