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Exam #3 Information

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.


Some basic information (but NOT a substitute for reading the book and reworking the homework problems):

  1. Practical Optimization Problems.
    1. 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.
    2. Pay attention to the domain of your function.
    3. 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.
  2. Exponential Functions.
    1. tex2html_wrap_inline71 .
    2. tex2html_wrap_inline73 .
    3. tex2html_wrap_inline75 if tex2html_wrap_inline77 .
    4. tex2html_wrap_inline79 .
    5. tex2html_wrap_inline81 .
    6. tex2html_wrap_inline83 .
    7. Know what the graph of tex2html_wrap_inline85 looks like when a>1 and when a<1.
    8. tex2html_wrap_inline91 .
    9. tex2html_wrap_inline93 .
    10. tex2html_wrap_inline95 .
    11. tex2html_wrap_inline97 .
  3. Exponential Models
    1. Exponential growth: tex2html_wrap_inline99 , k>0.
    2. Exponential decay: tex2html_wrap_inline103 , k>0.
    3. Learning curves: tex2html_wrap_inline107 , A,B,k>0.
    4. Logistic curves: tex2html_wrap_inline111 , A,B,k>0.
  4. The Natural Logarithm
    1. tex2html_wrap_inline115 means tex2html_wrap_inline117 .
    2. tex2html_wrap_inline119 is only defined for x>0.
    3. tex2html_wrap_inline123 .
    4. tex2html_wrap_inline125 .
    5. tex2html_wrap_inline127 .
    6. tex2html_wrap_inline129 .
    7. The graph of tex2html_wrap_inline131 is obtained by reflecting the graph of tex2html_wrap_inline133 across the line y=x.
    8. tex2html_wrap_inline137 .
    9. tex2html_wrap_inline139 .
    10. tex2html_wrap_inline141 .
    11. tex2html_wrap_inline143 .
  5. Differentiation of Logarithmic and Exponential Functions
    1. tex2html_wrap_inline145 .
    2. tex2html_wrap_inline147 .
    3. If tex2html_wrap_inline99 then Q'(t)=kQ(t) and tex2html_wrap_inline153 is the constant percentage 100k.
    4. Logarithmic differentiation.
  6. Interest
    1. Simple interest: no interest is earned on any interest. B(t)=P(1+rt).
    2. Compound interest, k times each year: tex2html_wrap_inline161 .
    3. Continuously compounded interest: tex2html_wrap_inline163 .
    4. Effective interest rate:
      1. For interest compounded k times each year: tex2html_wrap_inline167 (as a decimal).
      2. For interest compounded continuously: tex2html_wrap_inline169 (as a decimal).
    5. The present value of B dollars payable t years from now is tex2html_wrap_inline175 or tex2html_wrap_inline177 .
    6. 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.
    7. 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.
    8. Amortization of debt: tex2html_wrap_inline179 . 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.

next up previous
Next: About this document

Carl Lee
Tue Nov 10 08:47:50 EST 1998