Algebra Review - Chapter 8
1. The amount of money, A, accrued at the end of n years when a certain amount, P, is invested at a compound
annual rate, r, is given by
. If a person invests $240 in an account that pays 8% interest
compounded annually, find the balance after 10 years.
2. How much money must be deposited now in an account paying 7% annual interest, compounded yearly, to
have a balance of $1000 after 6 years?
3. Write an exponential function to model the situation. Then estimate the value of the function after 5 years (to
the nearest whole number). A population of 290 animals that increases at an annual rate of 9%.
4. The enrollment at Alpha-Beta School District has been declining 3% each year from 1994 to 2000. If the
enrollment in 1994 was 2583, write and solve an exponential equation to find the 2000 enrollment.
5. Explain the difference between a linear function and an exponential function when the functions are
represented in the following ways.
a. by equations
b. by graphs
c. by tables
6. The cost of a hamburger at a certain restaurant has increased exponentially over the d decades since 1951
when the restaurant first opened. A function that models the cost is
.
a) Rewrite the equation to give the cost of a hamburger in terms of y years after 1951 instead of d decades.
b) Use your equation for part a to estimate the cost of a hamburger at the restaurant in 1996.
c) Do you think your estimate in part b is reasonable? Does the function give a reasonable estimate for the
cost of a hamburger four decades from now? Explain.
____
7. Which of the following is equal to 1 when multiplied by
a.
b.
c.
?
d.
8. Malcolm invested $3000 in a small company. He predicts that the value of his investment will increase by 7%
per year. Assume that his prediction is correct.
a. Write a function that represents the value of Malcolm's investment over time.
b. Make a table showing the value of his investment after 0, 1, 2, and 3 years. Round to the nearest dollar.
c. After how many years will the value of Malcolm's investment be more than double his initial investment of
$3000? Explain.
Write a rule for the function.
9.
10.
11.
x
y
22
24
21
12
0
6
1
3
2
12. Last year a large trucking company delivered about 5 million loads of goods at an average value of $12,500
per load. What was the total value of goods delivered? Express your answer in scientific notation.
13. Evaluate
14. Evaluate
15. Graph the function:
and write the result in both standard form and scientific notation.
. Write the result in scientific notation.
. Then sketch the graph of
on the same grid.
16. Rewrite using only positive exponents:
a)
b)
c)
d)
____ 17.
a.
b.
c.
d.
____ 18. Which list shows the numbers in order from least to greatest?
a.
b.
c.
d.
19. Simplify:
a)
20. Write the expression
c) –(3 )2
b)
d)
in simplest form. Then write a different expression that involves division of
exponents that is equivalent to
. Justify your answer.
21. Graph the function and label as exponential growth or decay.
.
Then sketch the graph of
.
Tell whether the graph represents exponential growth or exponential decay . Then write a rule for the
function.
22.
23. Write
as a single power of 3.
____ 24.
a.
b.
c.
d.
Algebra Review - Chapter 8
Answer Section
1. $518
2. $666.34
3. f(x) =
; 446
4.
; y = 2152
5. a. A linear function can be written in the form y = ax + b. An exponential function is written in the form
.
b. The graph of a linear function is a straight line. The graph of an exponential function is a curve.
c. In a linear function, the differences between the corresponding y-values of consecutive x-values are the
same. In an exponential function, the quotients of the corresponding y-values of consecutive x-values are the
same.
6. a)
b) about $1.55
c) Sample answer: Yes, this estimate is reasonable. Hamburgers in some restaurants cost even more than this
now, so $1.55 seems reasonable. No, the estimate of the cost of a hamburger four decades from now is almost
$8, which seems unrealistically high.
7. A
8. a.
where y is the the value of Malcolm's investment after t years.
b.
c. After about 11 years; sample: Extend the table from part (b) for larger values of t. After 10 years, for
example, the value of Malcolm's investment is about $5902. After 11 years, he has about $6315, which is
more than double the value of his initial investment of $3000.
9.
10.
11.
12. $
13. 0.00000734 or
14. 1.66 x 10^8
15.
16. a)
c) –
b)
d)
17. C
18. C
19. a)
b) -5
20.
c)
d)
; sample:
. To divide powers with the same base, subtract the exponents.
21.
exponential decay
22. a) Exponential growth;
b) Exponential decay;
23.
24. C
or