Download Chapter 5 Review

Chapter 5 Review
Precalculus
Simplify each expression:
1.) a.) (-7)-2
b.) -7-2
2.) a.) 3  23
b.)  3  2 
3.) a.)
4 f 
4.) a.)
a
 3a 
 4a 
2 2
5.)
b.)  4  f 1 
1 1
1
1 2
 b 1 
3
2
1
b.)  a 1  b 1 
2
2
 b  a
6.)  2   2 
a  b 
3
Section 5.2 Rational Exponents
Write each expression using a radical sign and no negative exponents.
7.) a.) x
5
2
b.) x
1
3
2
5
c.) 6  y

1
3
Write each expression using positive rational exponents.
8.) a.)
x7
b.)
5
y2
c.)

3
5a

5
d.)
x4 x6 x
Simplify.
1
 25  2
9.)  
 36 
 25 
b.)  
 36 

1
2
5
 25  2
c.)  
 36 
 25 
d.)  
 36 
1.5
Word Problem
10.) The cost of a certain musical instrument has been increasing at 3% per year.
If the instrument now costs $15,000, find the cost:
a.) 3 years and 4 months from now.
b.) 2 years and 6 months ago (will be a negative time value).
Simplify
1
 32

11.) a  a  2a 2 


3
2
4
 13

3
2n  3n  4n 


12.)
1

2n 3
1
3
Solve.
13.) 94 x  81
14.) 8x1  2 x1
1 x
15.) 27
1
 
9
2 x
16.) a.)  8 x   64
3
b.) 8 x 3  64
c.) 8  x   64
3
5.3 Exponential Functions
Find an exponential function having the given values.
17.) f(0) = 3, f(2) = 48
18.) f(0) = 10, f(3) = 80
19.) The half-life of Carbon-14 is about 5700 years. If 1 kg is present now, how
much will be present after:
a.) t years?
b.) 11,400 years
Section 5.4 The Number e and the Function ex
20.) Using a calculator, evaluate:
a.) e0.07
b.) e3/2
21.) Suppose that $1000 is invested at 7% interest compounded continuously.
How much money would be in the bank after 5 years?
22.) A population of bacteria rapidly multiplies so that the population t hours from
now is given by A(t) = 300 e0.02t.
a.) How many bacteria are present now (now being the beginning)?
b.) How many will there be after one complete day?
Section 5.5 Logarithms
Write each equation in exponential form.
23.) log4 16 = 2
 1 
24.) log6   = -2
 36 
Solve for x.
25.) Solve 10x = 5 to the nearest hundredth.
x = ____________
26.) Solve 10x = 0.632 to the nearest hundredth. x = ____________
Find each logarithm. (Do not use a calculator).
27.) a.) log 100 = ______
b.) log 0.001 = ______
28.) a.) log6 36 = ______
b.) log36 6 = _____
29.) solve each to the nearest 1/100:
a.) ex = 12
b.) ex = 0.06
For the following, find each logarithm (do not use a calculator)
1
30.) a.) lne
b.) ln e2
c.) ln
d.) ln
e
31.) a.) log 105
b.) log225
c.) log555
e
d.) lne5
32.) Given ln10  2.3026, find:
a.) ln 0.1
b.) ln 0.01
c.) ln 100
Write each expression as a rational number or as a single logarithm.
33.) log 6 + log 2 + log 3
34.)
1
log6 16  log6 2
2
35.) 2 ln 6 – ln 4
Simplify each expression
36.) a.) ln e2
b.) ln e3
c.) ln
Express y in terms of x.
37.) log y = 2 log x
38.) ln y – ln x = 2 ln 7
1
e
Find the value of x to the nearest hundredth
39.) 2x = 100
40.) (0.98)x = 0.5
41.) ex = 18
42.) Tell how long it takes for $100 to become $1000 if it is invested at 8%
interest compounded:
a.) Annually
b.) Quarterly
c.) Continuously
43.) a.) Find log6 88 by using the change-of-base formula.
b.) Find log6 88 by solving 6x = 88.