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Rate of Change

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all right we've been talking about proportional relationships and today we're going to talk about something called the rate of change but first a little factoid did you know in the elections in California for every 15 people that can vote 10 people do vote and 5 people don't out did you realize that out of every 15 people that can vote five out of those 15 just choose not to vote not to exercise their right to vote which is kind of like one out of every three people just decide now I don't want to cast that's kind of crazy but the reason I bring that up is because this is what's called a ratio and you know what ratios are erase you as a way to compare two different so in this case were comparing the number of people who can vote with the number of people who don't vote 5 out of 15 now ratios are comparisons of two different numbers so you could be at a party with 30 people and maybe you look around and you notice that out of 20 people at the party 20 or girls and 10 or guys so you would say that there's a 22-10 girl to guy ratio you're comparing the number set the number of guys and you might realized that a 22-10 girl to guy ratio would be like a 2 to 1 ratio right and basically ratios are like fractions you can reduce them but unlike a fraction we wouldn't simplify this and just put the number to right because two one is to a ratio you would leave as a numerator and a denominator you wouldn't get rid of the denominator because in a ratio the whole point is to compare two numbers together so it's a two-to-one ratio would you can also write this way or this way you can write ratios with a fraction or using a colon or you can just say the word or write the word to a two-to-one ratio should be review cuz I think we now what ratios are but just in case you know you could be comparing the number of girls to the number of guys with the tutu runway show or you could be using it to 1 ratio does it say that there to Starbucks at one street corner or you could be using the two to one ratio to compare the number of peanut butter cups that you can buy set the number of dollars that you would spend on those peanut butter cups and if you did something like this what we would be saying is that you can buy two peanut butter cups for $1 and this kind of a ratio is called a rate a rate is a ratio that compares different things so instead of just comparing voters to voters or people at a party to other people at a party now we're comparing peanut butter cups $2 we're conveyed turn two different things and that's what we call a rate okay so some other examples of rates would be if you are at a party 20 people and you had five pizzas for 20 people that's a rate that's a pizza per person rate or a person per Pizza rate you comparing two different things pizzas and people and you might go to the grocery store and buy some orange juice and the rate that you pay for orange juice is $4.99 for 96 oz of orange juice and since you're comparing money without oz of orange juice it's a rate because money and orange juice are two different things and another example of a rate would be the rate at which you travel maybe you travel 120 miles into lowers and since you're comparing miles and hours which are two different things that is considered a rate so irate just Compares two different kinds of things now a rate of change is the amount that one variable changes when another also changes so if you're traveling miles in 2 hours time is changing and distance is changing and this rate of change answers the question how much how much is the distance changing as the time is changing or you could think of it this way at what rate is the distance changing its chain sing at a rate of 120 miles per 2 hours because the distance changed a hundred and twenty miles while the time changed to powers and this ratio is what we would call a rate of change because it talks about the rate at which something is changing okay so this past summer I started collecting Pokemon cards yep that's right so I started off with six cards in the first week of what thing I had six Pokemon cards and then I got six more so bye week too I had 12 cards and then I just kept home turn myself some Pokemon cards and I got six more so by week 3 I had 18 Pokemon cards and then I got seven so bye week for I had 25 cards okay are these rates yeah cuz I'm comparing time with number of cards what was the rate of change in this scenario well hopefully you can see that for the first 3 weeks the rate of change was six words per week because I got six cards in the first week and I have 12 cards by the second week and I had 18 cards by the third week and 6/1 equals 12/2 which also equals 18 over 3 we would say that this tuition at a constant rate of change of 6 card per week I was gaining 6 cards per week the number of cards I had voice changing by 6 cards per week but then something kind of funky happen and then I got seven cards in the fourth week and that kind of threw off my rate of and now my rate of change wasn't a constant anymore because that does not equal 6/1  so just review a ratio is a comparison of two different numbers and it can be written as a fraction or with a colon we're with the word to a rate is a ratio that compares two different types of things like dollars per ounce or miles per peanut butter cups per dollar and then a rate of change which is the whole point of this video is how much one people changes as another changes like how the amount of Pokemon cards changes over time or how the consider you travel in a car changes over time so let's see if you can put this into action could you write a ratio wearing the number of academic classes you have to the number of non-academic classes you have meaning  math science English History kind of classes versus elective kind of classes  could you make a ratio out of that and then could you write that ratio in three different formats I bet you could do that pretty easily now how about a more challenging problem if you're starting salary at a new job is $40,000  nice and then after a year you get a raise to $46,000 a year and then by your fifth year you're making $64,000 a year what is the rate of change of your salary  try that and see what you come up with and we will talk about that tomorrow alright that's rate of change hope you wrote some good notes and if you have any questions jot'em down so that we can discuss them tomorrow

Uploaded by Jeff Marbut.

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