MATH 142 Business Math II, Week In Review
Spring, 2015, Problem Set 2 (1.3, 1.5, 3.1)
JoungDong Kim
(1-6) Solve for x.
x
1
1.
=8
4
2. 53x = 1254x−4
3. (3x+1)2 = 3
4. 7x
2 +2x
= 7−x
1
5. x2 52x = 52x
6. (x2 + x − 2)2x = 0
7. Your rich uncle has just given you a high school graduation present of $1 million. The present,
however, is in the form of a 40-year bond with an annual interest rate of 9% compounded annually.
The bond says that it will be worth $1 million in 40 years. What is this million-dollar gift worth
at the present time?
2
8. Suppose that $1,000 is deposited in a saving account at an annual rate of 5%. Guess the amount
in the account at the end of 1 year if interest is compounded (1) quarterly, (2) monthly, (3) daily,
(4) hourly.
9. One bank advertises a nominal rate of 6.5% compounded quarterly. A second bank advertises a
nominal rate of 6.6% compounded daily. What are the effective yields? In which bank would you
deposit your money?
3
10. An account earns an annual rate of r, expressed as a decimal, and is compounded quarterly. The
account initially has $1000 and five years later has $1500. What is r?
(11-15) Simplify
√
11. log 10
1
12. log √
10
13. 10log 2π
14. e0.5 ln 9
15.
√
3log3 2
4
(16-17) Write the given quantity in terms of log x, log y, and log z.
√
16. log xyz
x2 y 3
17. log √
z
18. Write 2 log x −
1
log y + log z as one logarithm.
2
5
(19-21) Solve for x.
19. 3 · 102−5x = 4
√
20. e
x
=4
21. log(log 4x) = 0
22. If an account has an annual yield of 8% compounded monthly, how log before the account doubles?
6
(23-25) Find lim− f (x), lim+ f (x), and lim f (x) at the indicated value for the indicated function.
x→a
23. a = 1, f (x) =


 x4 + x2 − 1
24. a = 2, f (x) =
x→a
x→a



 x3 − x + 1
if x < 1
if x > 1
x−2
|x − 2|




−x + 2




25. a = 1, f (x) =
0






 x2
if x < 1
if x = 1
if x > 1
7
(26-30) Find the indicated limits if they exist.
26. lim 13
x→0
27. lim (3x3 − 2x2 − 2x + 1)
x→2
x2 + 2
x→1 x2 − 2
28. lim
x2 − x − 2
x→2
x−2
29. lim
x2 + 4
x→−2 x + 2
30. lim
8