Honors Algebra 2 Comp Book Review

Honors Algebra 2 Comp Book Review
Unit 2: Exponential and Logarithmic Functions
VOCABULARY: Thoroughly explain each of the following terms within the context of this
unit.
asymptote
exponential decay
natural logarithm
natural number e
base
exponential growth
exponential equation
common logarithm
logarithmic equation
logarithm
NON-CALCULATOR
Tell whether the following function shows growth or decay. Then, sketch a graph of the
function.
1.
( )
2. ( )
( )
(
)
Write each exponential equation in logarithmic form.
3
3. 3  243
5
4. 1  9
0
1
5.    27
3
Write each logarithmic equation in exponential form.
6.
log 2 16  4
7. log10  1
8.
2  log0.6 0.36
Simplify by using properties of exponents, memorized exponents and mental math.
9.
log 0.5 0.25
12.
log 2 1
10.
1
log12  
 12 
13. ln e
x y
11. log 0.01
14. e
ln 4 x
Express each as a single logarithm and simplify.
15.
log 2 8  log 2 16
18.
log105  log104
16. log10  log 0.1
17.
log5 252
Sketch a graph of each equation.
19.
f ( x)  e x  5
20.
f ( x)  e x  3
21. y
log5 x
CALCULATOR
The following formulas may be used to answer the questions.
 r
A  P 1  
 n
nt
A  Pert
N  N0e kt
22. The student population in a small resort town has increased by 2% per year for the last
5 years. This year’s population is 765 students.
a) Will the function that represents this situation show growth or decay?
b) Suppose that the student population continues to follow the same trend. Write a
function to show the number of students as a function of the year, starting with the
current year.
c) Sketch a graph of the function. Be sure to label your axes!
d) Predict the number of students in 3 years.
e) Now using your calculator, graph and predict when the population will exceed 1000
students.
23. If a saving account earns 4.75% interest annually how much will a deposit of $4900 be
worth in 9 years if interest is compounded monthly? Compounded daily?
Evaluate.
24.
25.
log3 15
log8 21
Solve each algebraically. Be sure to show work and check your answer.
26. 3
x1

1
9
27.
2x  4x1
28.
log 6 (2 x  3)  3
29.
 x
log 50  log    2
2
30.
ln x  2  5
31.
log3 (4 x  9)  5
Solve graphically.
32. log x
34.
5
x
2
 2.5
2ln x  ln x  3
1
33.    64
2
35.
log x  log( x  2)  4
36. The population of whooping cranes was about 22 in 1940 and grew at a rate of 3.5% to
about 194 in 2003. Use the exponential growth function
P(t )  P0ekt , where P0 is the initial
population and P(t) is the population at time t, to answer the following questions.
a) If the flock continues to grow at the same rate, how large will it be in 2020?
b) When will the population reach 300? Solve algebraically and show your work.
37. A headache medicine is eliminated from the bloodstream at a rate of 12% per hour.
Suppose you take a 20 mg tablet at 4:00 pm.
a) Write an equation that models the amount of medicine in the bloodstream.
b) How many mg of medicine are left in the bloodstream at 5:30 pm?
c) How many hours will it take for half the medicine to be eliminated?
38. The radioactive isotope Germanium-71 has a half-life of about 15 days.
a) Using N (t )
N0e
kt
, find the decay constant if a scientist has an initial amount of
25 grams.
b) Using your equation, how long until only 1 gram remains? Show your work!
39. Determine whether f is an exponential function of
the constant ratio.
x
f(x)
-1
0.667
0
1
1
1.5
x
of the form
2
2.25
f ( x)  ab x . If so, find
3
3.375
40. The following table gives the population size of a flock of birds in one habitat over the
last 57 years.
Years Since Data was First Collected
Population Size
5
18
22
22
40
85
57
185
a) Use exponential regression to find an exponential model for the data. Give the
equation below:
b) Use logarithmic regression to find a logarithmic model for the data. Give the
equation below:
c) Using a scatterplot of the graph of the data along with the equations, which do
you think is a better fit? EXPLAIN.
d) Using the equation you chose in part c, predict the population size 65 years after
the data was first collected.
e) How long will it take for the population to reach 240?