SEND - IN ASSIGNMENT
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REVIEW ASSIGNMENT
EXPONENTIAL AND LOGARITHMIC FUNCTIONS
Total ______ = _________%
Name: _________________________________________
Teacher:________________________________________
School:_________________________________________
59
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Show all work where possible for full marks.
1. Without graphing, which of the following functions increases at a faster rate? Explain why.
a. b.
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2. Compare the number of intercepts and end behavior of an exponential function in the form
( )= xy A b , where 0>A , and 0 1<
to the polynomial where the highest degree term is 32− x ,
and the constant term is 4.
Polynomial
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Exponential
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3. Using the equation of this function describe the following characteristics of its graph:
i) Base
i) ______________________
ii) Equation of the asymptote
ii) ______________________
iii) x-intercepts
iii) ______________________
iv) y–intercept
iv) ______________________
v) End behavior
v) _________________________________________________
vi) Domain
vi) ______________________
vii) Range
vii) ______________________
log ( )=y x ln ( )=y x
2 marks
2 marks
2 marks
1( ) 5
3
= −
x
f x
(7 marks)
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b. What parameter could you manipulate to change the direction of the function? If the
direction was changed, list any new characteristics of the graph.
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4. Match each function with the given graph. Explain your reasoning.
XXXXXXXXXXln( ) ) log ( ) 4
1 11
2 34
x
x
i y ii y e iii y x iv y x= − = = = +
2 marks
Function:
(2 marks each)
Reason:
Function:
Reason:
Function:
Reason:
Function:
Reason:
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5. List the similarities and differences in the two functions below in terms of the x-intercept(s), the y-
intercepts, domain, range, base, equation of the asymptote and end behaviour for the following:
6. An aftershock measuring 5.5 on the Richter scale occu
ed south of Christchurch, New Zealand in
June 2011. The magnitude, M of an earthquake that is T times more intense than an earthquake
measuring 5.5 on the Richter scale can be modeled by the following function: ( )log 5.5= +M T . For
every one unit of increase on the Richter scale, the intensity of an earthquake increases 10 fold.
a) Graph the function, [show window] and determine how much more intense an earthquake
XXXXXXXXXXmeasuring 7.7 that occu
ed on Queen Charlotte Islands in October 2012 was than the
XXXXXXXXXXaftershock in New Zealand.
a) ______________________
b) Determine the value of the function at 3=T , explain the answer in the context of this question.
b) _____________________________________________________________________________
Similarities Differences
( ) ( )a) 2 log 4b) ln
3
= − =y x y x
(5 marks)
2 marks
2 marks
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c) How many times as intense would an earthquake measuring 8.5 on the Richter scale be then one
XXXXXXXXXXmeasuring 5.5? Express your answer as a power with base 10.
c) ______________________
7. A $5000 investment that grows at annual rate of 6% can be modeled by the function: y = XXXXXXXXXXx
a) Determine the value of the investment after 20 years.
a) ______________________
b) How long would it take for the investment to double? Use your graphing calculator and show
window dimensions and graph.
b) ______________________
c) How long would it take the investment to double using the rule of 72? Explain any differences.
c) ______________________________________________________________________________
2 marks
2 marks
2 marks
WINDOW
Xmin = ________
Xmax = _______
Xscl = _________
Ymin = ________
Ymax = ________
Yscl = ________
Xres = ________
GRAPH (sketch)
2 marks
2 marks
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8. a) Would the future value of a $1000 investment be better represented by an increasing exponential
function or an increasing logarithmic function? Give reasons for your choice.
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b) What would the dependent and independent variables be in either case? Give reasons for your
XXXXXXXXXXchoice.
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c) Would there have to any restrictions on the domain or range in the function you used? Give reasons
XXXXXXXXXXfor your choice.
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9. The population of Su
ey, BC is shown in the table below for the years 1986 through 2011 in five
XXXXXXXXXXyear increments. Su
ey incorporated in 1879 with fewer than two hundred citizens.
a) Create a scatter plot of this data to show how the population is related to the year. Sketch the
scatter plot graph in the space provided.
2 marks
2 marks
2 marks
2 marks
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b) Determine an equation for a logarithmic regression function that would model this data.
b) _________________________
XXXXXXXXXXc) Describe the end behaviour.
c) _________________________________________________________________
_________________________________________________________________
d)