Math 103. Homework 6. Due 3/20/02

1. [Exercise 55, page 195] An economy's consumer price index (CPI) is described by the function

I(t) = -(0.2) t3+ 3t2 +100,        (0 £ t £ 10)

where t=0 corresponds to 1989.

(a) At what rate was the CPI changing in 1994? In 1996? In 1999?
(b) What was the average rate of increase in the CPI over the period from 1994 to 1999?

2. [Exercise 66, page 196] The percentage of U.S. population with portable phones is projected to be

P(t) = (24.4) t0.34        (1 £ t £ 10)

where t is measured in years and t=1 corresponds to 1998.

(a) What percentage of the U.S. population is expected to have portable phones by the beginning of 2006?
(b) How fast is the percentage of the U.S. population with portable phones expected to be changing at the beginning of 2006?

3. [Exercise 55, page 207] From experience, the Emory Secretarial School knows that the average student taking Advanced Typing will progress according to the rule

N(t)= 60 t+180 t+6        (t ³ 0)

where N(t) measures the number of words per minute the student can type after t weeks in the course.

(a) Find the derivative N¢(t).
(b) Compute N¢(t) for t=1,3,4 and 7 and interpret your results.
(c) Sketch the graph of N(t). Does it confirm the results obtained in part (b)?
(d) What will be the average student's typing speed at the end of the 12 week course?

4. The registrar of Kellogg University estimates that the total number of students enrollment in the Continuing Education division will be given by

N(t) = - 20,000 (1+0.2t)1/2 +21,000

where N(t) denotes the number of students enrolled in the division t years from now.

(a) Find an expression fro N¢(t)
(b) How fast is the student enrollment increasing currently? 5 years from now?
(c) How many students are currently enrolled? How many will be enrolled 5 years from now?

5. [Exercise 76, page 222] The quantity demanded per month, x, of a certain make of PC is related to the average unit price, p (in dollars), of PCs by the equation

x=f(p) = 100 9 (810,000-p2)1/2

It is estimated that t months from now, the average price of a PC will be given by

p(t) = 3200 8+t1/2 +200        (0 £ t £ 60)

dollars.

(a) What is the quantity demanded per month of the PCs 16 months from now? 25 months?
(b) Find the rate at which the quantity demanded per month of the PCs will be changing 16 months from now and 25 months from now.

Suggested Problems.- Section 3.1.- 41, 46, 47, 48, 57, 61, 62. Section 3.2.- 41, 51, 54, 56, 25, 28, 29, 30. Section 3.3.- 19, 32, 42, 55, 60, 68, 76. Section 3.4.- 8, 10, 12, 14, 16, 28, 32.