Math 55(31) - Warren D. Smith - Homework #5 - due Tues 4 March 2003
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read 8A, 8B. Warning: MIDTERM will be on March 6.

CONCEPTS:

The main thing to learn is

An exponentially growing quantity with doubling time T, will
increase in time t, to an amount
                                                    t/T
                     FinalAmount = InitialAmount * 2    .

Or if it is a HALVING time T, then after time t, the    t/T
amount of stuff instead will get DIVIDED by            2.

If a quantity is growing so its gets multiplied by c each year
for some c>1, then its doubling time is
                      DoublingTime = log(2) / log(c)   years.
years.  [If c=1+i  (i is the "interest rate"), the doubling time
is approximately                      .7/i  (i is a decimal)
          or                          70/i  (i is a percentage)
which the book calls the "rule of 70." I do not recommend using
the rule of 70 because it is only approximate. I recommend 
using my exact formula.]

If a quantity is decaying so its gets multiplied by c each year
by c with 0<c<1, then its halving time is
                      HalfLife = log(1/2) / log(1/c)   years.

Important facts about logs are on page 476 of book.

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Exercises chap 8B (p. 477-478):

Do #3 (and explain how you did it). 
Hint: you will need the properties
of logs on page 476.

Do #17 and #19 BUT do them with BOTH the "rule of 70"
(as the book asks) and ALSO with the exact formula (above), and compare your
two answers.   

Also do #25 and #29.