Welcome to Math 111 Algebra in Business and

Welcome to Math 111 Algebra in Business and Economics Instructor: Alexandra Nichifor Class Website: http: //www. math. washington. edu/~nichifor/111 F 06. htm Please pick up a copy of the syllabus and today’s handout

Worksheet 1: Speed as a Rate of Change

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

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

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

On the graph: 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 Rise Run

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

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

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

• 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.

ATS= Slope of Diagonal Line Rise=350 Tip: Can pick any two points on this line to compute the slope! 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

…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.