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Assessments
Unit 6: Exponential and Logarithmic Functions End Checkpoint Apply
– Unit 5: Rational Functions
Project
Unit 6: End Checkpoint Apply
Unit 6: Exponential and Logarithmic Functions End Checkpoint Apply
Interactive Tools
Lesson 3-5
Algebra 2
Please complete the following questions. It is important that you show all work you did to solve
the problems when you submit your work. This includes any calculations, diagrams, or graphs
that helped you solve it.
1. REASONING Use the properties of exponents to prove the Power Property of Logarithms.
2. OPEN ENDED Give an example of a quantity that grows or decays at a fixed rate. Write a
real-world problem involving the rate and solve by using logarithms.
3. Writing in Math Use the information about banking on page 556 to explain how the natural base e is used in banking.
Include an explanation of how to calculate the value of an account whose interest is compounded continuously, and an
explanation of how to use natural logarithms to find the time at which the account will have a specified value in your
answer.
Your Answer …
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11:51 AM
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x American High School | CC1
S Live Discussion – Studypool
CC – Algebra 2
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To develop an equation to
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an account increasingly larger
numbers of compounding
periods. Use a principal otsi,
an interest rater of 100 or 1,
and time of year
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Base e and Natural Logarithms in the table above, as increases the
prescimen 111 + 1, "cor (1 + i spproaches the irrational mamber
71878... This number is relerred to as the natural base,
You an write an equivalent baserponenti
luga unic equation in VEDE Y IN
Y
An exponential function with base e is called a
natural base exponential function. The graph of
y-r' is shown at the right. Natural base
exponential functions are wat extensively in
since to model quantities that grow and decay
coatinuously
Most calculators have an e' fanction for
evaluating natural base expressions
EXAMPLE Write Equivalent Expressions
Write an equivalent exponential or logarithmic equation.
a = 5
b. In: 0.6931
-
5log 5Y In x 0.61131 - log ry 0.6931
Dit 5 =
CHECK Your Progress
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38. In x l.2
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Since the raluralhase function and the natural logarithmic functionare
Invcrss, these two functions can be used to "undo' esch other.
Simplifying
Expressions
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EXAMPLE Evaluate Natural Base Expressions
O se a calculator to evaluate each expression to four decimal places.
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