Rate of Change

ConceptsSports

RateA ratio used to compare different kinds of

measurements.Ratio’s are frequently seen in things such as

insurance rates, housing, clothing, sales and sports.

Rate is ….

Sometimes it is anyways. Different kinds of rates are…

The change in YThe change in X

Point to Point AnalysisPoint to point analysis is when you find the

consecutive changes between numbers. Their first game, the Dallas Cowboys play the

Chicago bears and win 42-0.(We hope there are no Bears fans in here) And then they play their second game against the Steelers and they win 52-24. The Point to

Point Analysis is 10 1

Games

Score

1

2

42

52

Input OutputIf you find consecutive changes, you are able

to determine what kind of graph it is.i.e.= if it is increasing at a constant rate,

increasing at a fluctuating rate, decreasing at a constant, decreasing at a decreasing rate.

Positive slope, Negative slopeincreasing at a decreasing at a constant rate constant rate

Example: Increasing or Decreasing at Increasing or Decreasing ratesInput (also known as X, independent, domain)

in this scenario is the games played by a team.

Output (range, Y, dependent) is the team scores in the following scenarios.

Games the Cardinals Played

Score

1 24

2 32

3 42

Increasing at an increasing rate

Games the Steelers played

Score

1 12

2 24

3 35

Increasing at a decreasing rate

Average Rate of ChangeAverage rate of change is…Well, the average rate of change.Specifically, it is the change in the value of a

quantity divided by the elapsed time (or whatever Y is)

The steps to finding it go something like this.First, find the point to point rates on a graph.Then subtract the first number from the last

and divide.

Graph SketchThis one really doesn’t have an adequate way

of defining, so examples work just great for this one.

In the Olympics, a track runner runs the 400 in 46 seconds. He speeds up, speeds up some more and then sprints.

Speed of the RunnerSpeed

Time

Independent and Dependent variablesAn independent variable is a variable that can

stand alone and not be affected by the Y variable. Time is often considered an X variable.

Dependent variables are affected by X and cannot stand alone.

EXAMPLE!!!!!How many tickets to the Suns game are sold

depends on the price.Independent: Price.Dependent: How many tickets are sold.

Unit RateUnit rate is a rate in which the denominator

can be described with one.Common examples of a unit rate…11 soccer players

one field

2 cars

One track

Percent ChangeIs a way to express change in a variable.To find the percent change, it is best to first

find the difference between variables, then divide the difference by the original amount.

So if the baseball team has 300 bats and then 123 of them are broken in games or practice, what is the percent change?

300-123=177177/300=.5959% change

Domain and RangeDomain (also known as X) is the X set of

values in an equation. So if there are 4 badminton games and the scores are 15, 14, 5 and 27

Domain would be 1, 2, 3 and 4 because that’s the number of games.

Range is otherwise known as Y and that would be the scores they received. 5, 14, 15 and 27.

So all in all, set into an equation it would look something like this.

D{1,2,3,4} R {5, 14, 15, 27}

And the icing on the top of the cake of Domain and Range is, Practical and Actual Domain and RangeActual domain and range is what is directly indicated on the graph or

table.Practical is what is reasonable for the given situation Practical: 0<y< 25

0<x<infinity Actual: D{1.2.3.4}

R{3,10,18,22}2520 15105 1 2 3 4