1. Welcome to Math 111 Algebra in Business and Economics Instructor: Alexandra Nichifor Class Website: http://www.math.washington.edu/~nichifor/111F06.htm Please pick up a copy of the syllabus and today’s handout

2. Worksheet 1: Speed as a Rate of Change

3. Time t (minutes) Distance D travelled (miles) after time t 0 10 20 30 40 50 60 70 75 0 120 170 180 205 280 430 550 Q?: How far did the rocket travel from 50min to 60min? A: 75 miles 205 280 280-205=75

4. Delta Notation: Greek letter Delta: is shorthand for “the change in” Example: How far did the rocket travel from 50min to 60min?

5. Q: What was the average speed of the rocket from t=50 min to t=60 min? average speed = Change in distance Change in time Shorthand (  =change in…) miles per minute

6. On the graph: Rise Run Moral: Average Speed (AS) from time t 1 to time t 2 =slope of the secant line thru the graph of the distance at points t 1 & t 2

7. A rate of change is a measure of how fast a quantity is changing with respect to time Examples?

8. VIP Example: average speed is a rate of change of distance. average speed = Change in distance Change in time In general: Average Rate of Change of Blah = Change in Blah Change in time

9. Types of Rates of Change: Average Rate of Change Actual (Instantaneous) (will study in Math 112) Example: Actual speed, as read off a speedometer Overall (from t=0 to later time ) Incremental (from t=a to t=b) Example: Average Trip Speed (ATS) Example: Average Speed (AS)

10. Note: An overall rate of change (such as ATS) is a special case of an incremental rate of change. that is, one in which the initial time t 1 =0. Question: How do we measure the ATS on a graph of distance? For example, on our handout, what was the ATS over the first hour? Answer: Compute the slope of the line from the beginning of the graph (t 1 =0) to t 2 =60 min.

11. ATS= Slope of Diagonal Line Tip: Can pick any two points on this line to compute the slope! Rise=350 Run=75 Answer: ATS over the first hour = 350 / 75 = 4.67 mpm = 280 mph Note: Using the original two points: 280 / 60 =4.67 mpm

12. …To be continued on Friday… Homework for Friday: 1.Familiarize yourself with the class rules by carefully reading the syllabus and the class website. 2.Print the Lecture Handouts (and bring to class!) 3.Get the text, a ruler, and a scientific calculator. 4.Read and do the problems in the Prologue. 5.Start working on Worksheet 1.