**Exam #3 Information
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The exam will be Wednesday, November 18, 5-7 pm, in Memorial Hall.
Questions will be drawn from Sections 3.4 and 4.1-4.5. Calculators
are permitted, but you will still have to show your work.
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BE SURE YOU CAN DO ALL THE HOMEWORK PROBLEMS QUICKLY AND CONFIDENTLY
WITHOUT LOOKING AT YOUR NOTES OR AT THE BOOK.
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Some basic information (but NOT a substitute for reading the book and
reworking the homework problems):
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**Practical Optimization Problems.**- Find a function of a single variable to maximize or minimize. You may have a function of two variables and need to use some other equation to eliminate of the variables from your function.
- Pay attention to the domain of your function.
- After you have found the first order critical numbers, remember to check using the first or second derivative tests whether you have a maximum or minimum at the various points. Don't forget to check the endpoints of your domain if you have any.

**Exponential Functions.**- .
- .
- if .
- .
- .
- .
- Know what the graph of looks like when
*a*>1 and when*a*<1. - .
- .
- .
- .

**Exponential Models**- Exponential growth: ,
*k*>0. - Exponential decay: ,
*k*>0. - Learning curves: ,
*A*,*B*,*k*>0. - Logistic curves: ,
*A*,*B*,*k*>0.

- Exponential growth: ,
**The Natural Logarithm**- means .
- is only defined for
*x*>0. - .
- .
- .
- .
- The graph of is obtained by reflecting the graph of
across the line
*y*=*x*. - .
- .
- .
- .

**Differentiation of Logarithmic and Exponential Functions**- .
- .
- If then
*Q*'(*t*)=*kQ*(*t*) and is the constant percentage 100*k*. - Logarithmic differentiation.

**Interest**- Simple interest: no interest is earned on any interest.
*B*(*t*)=*P*(1+*rt*). - Compound interest,
*k*times each year: . - Continuously compounded interest: .
- Effective interest rate:
- For interest compounded
*k*times each year: (as a decimal). - For interest compounded continuously: (as a decimal).

- For interest compounded
- The present value of
*B*dollars payable*t*years from now is or . - The present value of an annuity that consists of a periodic sequence of payments over a specified term is the amount of money that must be deposited today to permit periodic withdrawals generating the same sequence of payments over the specified term, after which nothing will be left in the account.
- Optimal holding time: When the percent rate of growth of the value of an asset ceases to be greater than the prevailing interest rate, and begins to be less than the prevailing interest rate. Equivalently, when the present value of the value of the asset is greatest.
- Amortization of debt: .
*A*is the amount of the loan,*r*is the interest rate (in decimal),*t*is the number of years,*M*is the monthly payment.

- Simple interest: no interest is earned on any interest.

Tue Nov 10 08:47:50 EST 1998