College Algebra Homework

Please REVIEW the topics and take a look at problems!! 12 math questions in which all work needs to be shown. Majority of the topics involved are the following:

  • Apply properties of logarithms and the change-of-base formula
  • Solve exponential and logarithmic equations and inequalities
  • Applying the mathematical modeling process to exponential models and logarithmic models
  • Dealing with functions
  • Domains and functions
  • Sketching a graph

All work must be shown and make sense. If you are not proficient or well-versed in these math categories, please do not accept. Thank you!

 

 

Math 107: Quiz #5: Name: ______________________________________

Due: 11/07/20

Please show all work. Each problem is worth 10 points.

 

1Sketch the graph of the given function, showing all necessary characteristics. This does not mean graph it from your calculators.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2. Find each of the following..

 

 

a. b. 

 

 

 

 

 

 

 

 

 

3a. Convert to an exponential equation.3bConvert to a logarithmic equation..

 

 

a. ln 0.38 = -0.9676 

 

 

 

 

 

 

 

 

 

 

 

 

 

c. Given that , 

 

Find 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4. Express in terms of sums and differences of logarithms. This means, expand.

 

 

 

 

 

 

 

 

 

 

 

 

5. Express as a single logarithm. This means, condense

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6. Solve the given equation.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7. Solve 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

8. The population of Panama was 3.039 million in 2005, and the exponential growth rate was 1.3% per year.

 

a. In what year will the population be 12 million?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

b. What is the doubling time?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

9. Suppose $3000 is invested at a rate k, compounded continuously, and grows to $3700.45 in 3 years, find the balance after 8 years.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

10. Find the inverse of the given function.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

11. The formula, occurs in theory of 

electricity. Solve for t.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

12. ,

 

a. . (the little circle means, composition of functions. It does not mean multiply.)

Do not forget that x must be in the domain of g and g(x) must be in the domain of f.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

b. .

64

log

2

125

1

5

3

=

609

.

1

5

log

,

845

.

0

3

log

,

693

.

0

2

log

»

»

»

b

b

b

and

b

b

15

log

3

2

log

N

M

)

ln

(ln

3

2

ln

y

x

x

+

27

1

3

4

2

=

+

x

x

x

x

x

3

3

3

log

)

6

(

log

)

14

(

log

=

+

+

ú

û

ù

ê

ë

é

=

t

L

R

e

R

V

i

)

(

1

4

log

64

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