Math 55(31) - Warren D. Smith - Homework #4 - due Tues 18 Feb 2003
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Finish reading all of chap 9A, 9B. Start reading chap 8A, 8B.
Upcoming tests: There will be a dept-wide midterm on Thur 6 March.
We will have an earlier quiz, sort of a pre-midterm, on
Tues 18 feb (same day this homework is due).
This quiz will cover everything in chap 4, and 9A, 9B and
maybe some stuff from 8A, 8B too.  

Exercises:

This HW I'm going to give you exercises like those in the book, but
not the same (I'm making them up myself this time). 

Ex 1.  (Like ex 1 p508 9A but not same.)
Draw axes and plot and label these points:
(0,5),  (-2,7),  (3,2),  (4,-3),  (-3, 5).

Ex 2.  Consider the function  F(x) = (x+7)/(38-x).
(a) What is the NAME of this function? 
(b) What letter in "F(x)" is playing the role of the INPUT
to this function?
(Hint: for both a and b, the answers are among "F", "G", "x" or "arctan.")
(c) What is F(23)?

                                      (x+3)/2  if x>5
Ex 3.  Consider the function  G(x) = {
                                      -77      if x<5
(a) What is the NAME of this function? 
(b) What is G(7)?
(c) What is G(2)?

Ex 4.   (Like ex 23 p522 9B but not same.)
The price of a bulldozer is $50000 today.
But 5 years ago, it cost $41000.  
(a) Assuming the price depends approximately LINEARly on time,
how much will a bulldozer cost in 4 years?
(b) If t is "number of years starting now"
(for example, 2 years ago t = -2) then what is a FORMULA
for  PriceOfBulldozer(t)?   Hint:  your formula should have the
property that    PriceOfBulldozer(4) = Your answer to (a).

Ex 5.  (Like ex 19-22 p522 9B but not same.)
Consider the equation     y = 2 x - 3.
(a) Sketch an x-y plot of this function. 
(b) What is its SLOPE?  
(c) What is its y-intercept?


Ex 6.   (Like ex 17 p522 9B but not same.)
Suppose it costs $34000 to buy a condo, and then it costs
$5000 per year in "fees" for every year thereafter.
Let t be the total number of years since you buy the condo.
What is a FORMULA  for  TotalMoneyYouPaidSoFar(t)?
Hint: Your formula should have the
property that     TotalMoneyYouPaidSoFar(0) = 34000.


Ex 7.  (Like ex 21 p468 8A, but more accurate).
The population of Earth is 6.5 billion.
It is doubling about every 40 years.
The total surface area of the Earth (only counting habitable land)
is about                                    14
          100 million square kilometers = 10  square meters.
Assume to grow enough food and produce enough resources 
for an average human to live off of, requires a 62meter X 62meter
square patch of land (about half the size of a football field).
HOW MANY years have we got (if this doubling rate continues) 
before humankind can no longer live?