Assignment 64
"He who wonders discovers that this in itself is a wonder". (M.C. Escher)
COUNTING AND COMPUTING DEVICES:
Human Fingers: Many cultures devised clever methods to use these everavailable counting and computing devices. Our fingers and toes total 20, accounting for some early 20base number systems.
Greek mechanical computer (?): In 1900, Greek fisherman found a corroded mechanism estimated to be 2,000 years old at the bottom of the Aegean Sea. It appeared to be part of a geared computerlike device.
Quipus: The Incas of fifteenth and sixteenth century South America used knotted and colored strings to keep complex records of everything from population to the amount of food a village needed to store for lean seasons.

Why wouldn't Herkimer supply a candle for the man who slept all day?
Answer: He believed there should be no wick for the rested.
Herky wants to know:
When a person says he is a "man of few words," why does he then use a few million of them?
If you make many mistakes in a single day, can you justify this by saying you got up early? 
ASSIGNMENT #64
Reading: Section 8.7, pages 509512.
Written: Page 515, problems 55 and 56. Use your calculator to fit both a power function y = ax^{b} and an exponential function y = ab^{x} to the data provided. See example in Items for reflection (below). Also, do the financial problems shown. 
Mathematical word analysis: PERMUTATION: From the Latin permutare ("to change"). In mathematics, a permutation is an arrangement change. There are six permutations of ABC, namely ABC, ACB, BAC, BCA, CAB, and CBA.  The table shows the atomic number x and the melting point y (in degrees Celsius) for the alkali metals.
ALKALI METAL 
Lithium 
Sodium 
Potassium 
Rubidium 
Cesium 
x = Atomic number 
3 
11 
19 
37 
55 
y = Melting point. 
180.5 
97.8 
63.7 
38.9 
28.5 
Using the TI83, here are the power and exponential fits.
POWER
y = ax^{b}
a = 397.6098
b = 0.6390
r^{2} = 0.9847 
EXPONENTIAL
y = ab^{x}
a = 152.3369
b = 0.9671
r^{2} = 0.9176 
Financialtype problems (Write these up in logarithmic form. Communicate.)
1. How long will it take money to triple if the interest rate is
(a) 8.2% compounded quarterly? (b) 8.2% compounded daily? (c) 8.2% compounded continuously.
2. How many years will it take a quantity to decrease to 10% of its original amount if the decay rate is
(a) 4% a year? (b) 11% a year? (C) 28% a year?
3. The gross domestic product (GPD) G (in billions of dollars ) can be modeled by the equation
G = 9700/(1 + 8.03e^{0.121t})
where t is the number of years since 1970. In what year was the GPD approximately $5000 billion?
Problem: If log y = 2x + 1, write y as a function of x.
Solution (with communication):
log y = 2x + 3
==> y = 10^{2x+3} =^{ }10^{2x}10^{3} = (10^{2})^{x}1000
==> y = 1000(100^{x}). 
Problem: If ln y = x + 2, express y as a function of x.
Solution (with communication):
ln y = x + 2
==> y = e^{x+2} = e^{x}e^{2}
==> y = 7.389e^{x}. 
