(Back to the practice test on tutorials 42 - 47)

College Algebra
Answer/Discussion to Practice Test 


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

 
1a.
 
Answer:

x
(x, y)
-2

(-2, .03)
-1

(-1, .17)
0

(0, 1)
1

(1, 6)
2

(2, 36)




 
 
1b.  
 
Answer:

x
(x, y)
-2

(-2, -36)
-1

(-1, -6)
0

(0, -1)
1

(1, -.17)
2

(2, -.03)




 
 
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.
 
Answer:

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


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 %.
 
 
Answer:

P = 4525
r = 9.5% = .095 
t = 12


So the accumulated or compound AMOUNT would be $14148.63.

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

 
4a.  
 
 
Answer:




 
4b.  
 
 
Answer:



 

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

 
5a.
 
 
Answer:





5b.
 
 
Answer:




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

 
6a.
 
 
Answer:




6b.
 
 
Answer:



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

 
7a.
 
 
Answer:


y
(x, y)

-2
(.01, -2)

-1
(.11, -1)

0
(1, 0)

1
(9, 1)

2
(81, 2)




 
7b.
 
 
Answer:



y
(x, y)

-2
(2.001, -2)

-1
(2.012, -1)

0
(2.11, 0)

1
(3, 1)

2
(11, 2)



 

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

 
8a.
 
 
Answer:



 
8b.
 
 
Answer:




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

 
9a.
 
 
Answer:



 
9b.
 
 
Answer:


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

 
10a.
 
 
Answer:

 



10b.
 
 
Answer:

 


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

 
11a.
 
 
Answer:



11b.
 
 
Answer:




 
11c.
 
 
Answer:



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. 
 
 
Answer:




 
12b. 
 
 
Answer:


x = 2 is the only solution.

 


(Back to the practice test on tutorials 42 - 47)


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Last revised on March 23, 2004 by Kim Seward.