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Virtual Math Lab

College Algebra
Answer/Discussion to Practice Problems  
Tutorial 48: Practice Test on Tutorials 42 - 47


 


Problems 1a - 1b: Graph the following functions.

 
1a. problem 1a
 
checkAnswer:

x
problem 1a
(x, y)
-2
ad1a1
(-2, .03)
-1
ad1a2
(-1, .17)
0
ad1a3
(0, 1)
1
ad1a3
(1, 6)
2
ad1a5
(2, 36)


ad1a6

 
 
1b.   problem 1b
 
checkAnswer:

x
problem 1b
(x, y)
-2
ad1b1
(-2, -36)
-1
ad1b2
(-1, -6)
0
ad1b3
(0, -1)
1
ad1b4
(1, -.17)
2
ad1b5
(2, -.03)


ad1b6

 
 
Problem 2a:   Find the 1) compound amount AND 2) the compound interest for the given investment and rate.

 
2a. $25000 for 21 years at an annual rate of 3.25% compounded quarterly.
 
checkAnswer:

P = 25000
r = 3.25% = .0325
t = 21
n = quarterly = 4 times a year

ad2a

Compound Amount: $49334.23
Compound Interest: $24334.23



 
 
Problem 3a: Find the accumulated value for the given investment and  rate.

 
3a. $4525 that is compounded continuously for 12 years at an interest rate of 9 ½ %.
 
 
checkAnswer:

P = 4525
r = 9.5% = .095 
t = 12

ad3a

So the accumulated or compound AMOUNT would be $14148.63.

 
 
Problems 4a - 4b: Express the given logarithmic equation exponentially.

 
4a.   problem 4a
 
 
checkAnswer:

ad4a


 

4b.   problem 4b
 
 
checkAnswer:

ad4b



 
Problems 5a - 5b:  Express the given exponential equation in a logarithmic form.

 
5a. problem 5a
 
 
checkAnswer:

ad5a


 

5b. problem 5b
 
 
checkAnswer:

ad5b


 
 
Problems 6a - 6b:   Evaluate the given log function without using a calculator. 

 
6a. problem 6a
 
 
checkAnswer:

ad6a


 

6b. problem 6b
 
 
checkAnswer:

ad6b


 
 
Problems 7a - 7b: Graph the following functions.

 
7a. problem 7a
 
 
checkAnswer:

ad7a1
y
(x, y)
ad7a2
-2
(.01, -2)
ad7a3
-1
(.11, -1)
ad7a4
0
(1, 0)
ad7a5
1
(9, 1)
ad7a6
2
(81, 2)


ad7a7


 

7b. problem 7b
 
 
checkAnswer:


ad7b1
y
(x, y)
ad7b2
-2
(2.001, -2)
ad7b3
-1
(2.012, -1)
ad7b4
0
(2.11, 0)
ad7b5
1
(3, 1)
ad7b6
2
(11, 2)


ad7b7



 
Problems 8a - 8b:   Evaluate the given expression without the use of a calculator.

 
8a. problem 8a
 
 
checkAnswer:

ad8a


 

8b. problem 8b
 
 
checkAnswer:

ad8b

 
 
Problems 9a - 9b:  Expand each logarithmic expression as much as possible.  Evaluate without a calculator where possible.

 
9a. problem 9a
 
 
checkAnswer:

ad9a


 

9b. problem 9b
 
 
checkAnswer:

ad9b

 
 
Problems 10a - 10b:  Condense each logarithmic expression into one  logarithmic expression.  Evaluate without a calculator  where possible.

 
10a. problem 10a
 
 
checkAnswer:

 ad10a


 

10b. problem 10b
 
 
checkAnswer:

 ad10b


 
 
Problems 11a - 11c:    Solve the given exponential equation.  Round your answer to two decimal places.

 
11a. problem 11a
 
 
checkAnswer:

ad11a


 

11b. problem 11b
 
 
checkAnswer:

ad11b



 
11c. problem 11c
 
 
checkAnswer:

ad11c

Since e raised to a power cannot equal a negative number, there is only one solution, x is approx 1.61.


 
Problems 12a - 12b:   Solve the logarithmic equation.  Round your answer to two decimal places.

 
12a.  problem 12a
 
 
checkAnswer:

ad12a


 

12b.  problem 12b
 
 
checkAnswer:

ad12b


x = 2 is the only solution.

 


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Last revised on March 25, 2011 by Kim Seward.
All contents copyright (C) 2002 - 2011, WTAMU and Kim Seward. All rights reserved.