08 Bases Other Than e Day 2.notebook

08 Bases Other Than e Day 2.notebook
April 07, 2014
Recall from last time, Derivative Formulas
Involving Logs & Exponential Functions
Log Rule Base "e" Log Rule Base "a" Expo. Rule Base "e" Expo. Rule Base "a" Exponential & Log Derivative Formulas
Recall:
Integral of "e"
­OR­
Integrals for base"a"
*These formulas you may want to add to
your Integrals Note Card!!
Integrals of bases other than "e"
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08 Bases Other Than e Day 2.notebook
April 07, 2014
Example: Find the Integral
1.
2.
"u" Substitution Examples
Compound Interest
Let P = pocket $$, t = number of years, r = annual interest rate (convert to a decimal), n = # of times a year interest is compounded A = value of account after t years
For interest compounded "n" times a year: For interest compounded continuously:
Compound Interest Formulas
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08 Bases Other Than e Day 2.notebook
April 07, 2014
Example:
$2500 is invested in an account that has a 7% interest rate. Find the amount of money in the account after 5 years if the account is compounded (a) annually, (b) quarterly, (c) monthly, (d) daily, and (e) continuously
A = ??, P = 2500, r = 7% (.07), t = 5
a) Annually means: n = 1
d) Daily means: n = 365
b) Quarterly means: n = 4
e) Conintuously means: A = Pert
c) Monthly means: n = 12
Easy Example
Example Involving Logs:
Compounding monthly at an interest rate of 12%, how long will it take for an account to double in value?
It appears we don't have
enough information. Let's
look at what we do know:
• r = 12% (.12),
• n = 12,
• t=t
What do we know about
A & P?
A will be 2 times P
ie: A = 2P
Example Involving Logs
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08 Bases Other Than e Day 2.notebook
April 07, 2014
Example Involving Limits
Suppose the yield V (in millions of cubic feet per acre) for a stand of timber at age "t" years is found to be:
(a) Find the limiting volume of wood per acre as t approaches infinity (ie: )
What happens to the exponent as "t" approaches ∞
the exponent goes to 0
Example Involving Limits
Example Involving Derivatives
Suppose the yield V (in millions of cubic feet per acre) for a stand of timber at age "t" years is found to be:
(b) Find the rate of change at which the yield is changing when t = 20 years and t = 60 years.
What does "rate of change" imply??
derivatives!!
Example Involving Derivatives
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08 Bases Other Than e Day 2.notebook
April 07, 2014
Homework:
p368 (#75-86 all, 95a&b, 105, 108,
121-123)
Homework
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