honcalc unit 7 exponential and log...
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HonCalc Unit 7 Exponential and Log Functions.notebook
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October 29, 2018
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Homework: pp. 478480
# 1114, 23, 25, 65, 66, 69, 72
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HonCalc Unit 7 Exponential and Log Functions.notebook
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HonCalc Unit 7 Exponential and Log Functions.notebook
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HonCalc Unit 7 Exponential and Log Functions.notebook
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Bell Ringer
Explain in words why this problem cannot be solved with common bases.
2x = 6Can you get a decimal approximation?
(hint use your calculator)
HonCalc Unit 7 Exponential and Log Functions.notebook
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One way we could do this is:
to graph y = 2x and y = 6 and see where they are equal.
looks like
(2.6 ish)
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Another way we can do this is to use the inverse of an exponential which is a logarithm.
What is a logarithm you say?
How does it work?
HonCalc Unit 7 Exponential and Log Functions.notebook
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7.2 LOGARITHMIC FUNCTIONS AND THEIR GRAPHS:
Lesson Goals:
1) I can recognize and evaluate log functions with base a
2) I can graph logarithmic functions
3) I can recognize, evaluate, and graph natural log functions
4) I can use log functions to model/solve realworld problems
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HonCalc Unit 7 Exponential and Log Functions.notebook
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A logarithmic expression really asks us a question: What exponent has to be put on the base to make it worth the argument?
ex) log2 ( 8) = 3base argument
exponent
This one is easy because we could figure out that the answer was 3. The usefulness of the log is that we can now find out answers (exponents) that were not easy like the bell ringer problem.
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Use your calculator:
Use Alpha, window and
choose logeBase
Try typing log2 8 and see what happens since you know the answer.
HonCalc Unit 7 Exponential and Log Functions.notebook
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2x = 6
log2(2x) = log2(6)
x = ______
We will take the log of both sides using the same base as my exponential expression.
Say it with me y'all:
"The base of the log is the base of the exponent"
Now what exponent has to be put on a 2
to make it look like 2x ?
So the answer to the left side of this
equation is just x.
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Remember the log is asking you a question:
what exponent do we need to make the base worth the argument the big number
HonCalc Unit 7 Exponential and Log Functions.notebook
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Evaluate each expression:
A) log 9 81
B) 3 log31
HonCalc Unit 7 Exponential and Log Functions.notebook
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The common log function is the inverse of the exponential function y=10x
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HonCalc Unit 7 Exponential and Log Functions.notebook
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GUIDED PRACTICE
Common Logs, Natural Logs
log 10,000 eln 4
log 0.081 ln ( )
log 0 ln 9
10log 3
ln 32
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GRAPHS of Log FunctionsOne way to graph it is to 1st graph the inverse, then use the TABLE function to grab some coordinates of the inverseuse those points to sketch the graph of the log function
Sketch and analyze each function's graph. Describe the domain, range, intercepts, asymptotes, end behavior, and where the function is increasing or decreasing
h(x) = log2x j(x) = log1/3x
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0<
Domain: (0,∞)
Range: (∞,∞)
yintercept : NONE
xintercept: 1
Extrema: NONE
Asymptote: yaxis
Continuity: continuous on (0,∞)
End Behavior:
HonCalc Unit 7 Exponential and Log Functions.notebook
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Use the graphs of f(x) = log x and f(x) = ln x to describe the transformation that results in each function. Then sketch the graphs of the functions.
k(x) = log (x+4)
m(x) = log x 5
p(x) = 3 log (x+2)
a(x) = ln (x6)
b(x) = 0.5ln x 2
c(x) = ln (x+4) + 3
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GUIDED PRACTICETECHNOLOGY The number of machines infected by a specific computer virus can be modeled by c(d) = 6.8 + 20.1 ln d, where d is the number of days since the first machine was infected.
A) About how many machines were infected on day 12?
B) How many more machines were infected on day 30 than day 12?
C) On about what day will the number of infected machines reach 75?
HonCalc Unit 7 Exponential and Log Functions.notebook
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HUMAN MEMORY MODEL:Students participating in a psychology experiment attended several lectures on a subject and were given an exam. Every month for a year after the exam, the students were retested ot see how much of the material they remembered The average scores for the group are gtiven by the human memory model f(t) = 75 6 ln (t + 1), 0 ≤ t ≤ 12 where t is the time in months. What was the average score at the end of t = 2 months? 6 months? on the original exam (t = 0)?
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Homework: pp. 488490,
# 39, 4550, 55, 60, 99, 100