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5/6/19 Midterm Study Guide Instructional video

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Re-take Midterm Tuesday, May 14.

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her students this is Miss Windham we are going to get through this midterm study guide and you are going to retake your meter you're going to do great right let's get right to it we have classifying and graphing functions the first one is y equals x with Y equals X you know that it crosses origin cuz this is like x + 0 so across is at the origin and has a slope of 1 so if you if you think about Crossing at the Orange in a slope of 1 you have a line that looks like that and it is a linear function number to y equals x squared when you have an expo it all it's not wine you know it is not linear with an exponent of 2 you know that it is a quadratic or we call it a parabola so this has a y-intercept of 1 and it goes up like that write a quadratic number 3 y equals 2 the power of X when you have your X in the exponent spot it is an exponential and it will very quickly guess I can put an arrow on the Arizona Coyotes the last one of this type number for y equals the absolute value of x + 2 this is absolute value you know that because of the bars the absolute value bars and when you have absolute value it's always going to be a value makes a vs2 inside of the bars that's actually a horizontal shift two places to the so it's going to start there at also has a slope of Y is a one so it looks like that writing linear equations number 31 write the equation for the graph I have a rise over run Tron here so the two thing do you need you to write an equation you need the Y intercept and that's the point where the line crosses the y-axis here's the x-axis and the other thing you need is the slope in the slope rise over run I have marked the rise in the run on this line because it's kind of hard to see these great lines so this slope going to be when you rise one and run one that's one over one which we will write as one and the point where it crosses the y-axis the cross is right there at 2 flower template is y is equal to MX plus b and we will substitute a one-in-four in and that will be an understood coefficient of the X and we'll put a 2 + 4 b + Y is equal to x + 2 or 1 X Plus to write 32 write the equation for the table of the first thing I need to do is make sure you were seven is an 8 right there okay so we we know that we have the y intercept when X is equal to 0 because if x is zero it's going to be right on the axis and we had that point right here that's going to be be right because he's going to be 18 now we need to find the slope of a slope how old is we take the wise to the wise and subtract them and that's in our numerator and then we take taxes and subtract them in our denominator so I can I go with 2 + 23 + say y over X 23 - 18 Ober 2-0 now I would this horizontal table you have to make sure you put your wise in the numerator and your ex is in the denominator so 23 I believe is a v 2-0 is just going to be too so our slope is 5/2 so we write the equation we're going to have y is equal to it doesn't matter that we have an improper fraction as our slope 5 / 2x + 18 so that's a pretty wicked little equation write 5/2 x + 80 number 33 a gaming club cost $45 to join that means one time fee each game that is rented cost $5 each game so that's a multiplication thing we are writing this equation it should be in slope intercept form I'm going to start with the Y intercept because that's going to be our starting point it's a one time fee $45 and then each time we went to game we pay $5 so ex is going to be me the number of games number of games rented equation then y equals 45 + 5 alright students were getting into the fun stuff now applications of slope and intercepts he starts out with 20 chicken nuggets and eat stew every minute lucky teeth alright so we have a starting point of 20 nuggets and eating to every minute that's a negative slope we are going to write y equals 20 - 2x right graph the equation let's think about our graph here and we're going to number and label things it will take a few minutes this is going to be minutes this is our independent quantity nothing affects time time is always independent these are the nuggets if I'm starting a 20 I guess I need to go up by twos and then I messed up dinner but 2 4 6 8 we start here and to every minute means go down that's just one grid line because that's two nuggets so our equation or graph looks like that and I don't have a line tool so my lines are not going to be very straight something like that right identify the slope the slope is a negative to a positive what does the slope represent the number of nuggets eaten per minute this per minute is important identify the Y intercept the Y intercept is 20 does it represent the number of nuggets we start with I'm going to say we the Royal we I guess extend I'm not finishing this with a preposition correct identify the x intercept okay well this is a little harder here but the x intercept is when Y is equal to 0 so let's steps to 0 + 4y and we have 20 - 2 x + let's solve for x which means we would subtract 20 / 0 20 is -20 equals -2X divided by -2 what is -20 divided by -2 well I know you know that it is a positive 10 so our excavator stepped is 10 what is it represent it represents the number of minutes it takes to eat all the knight swords it's how long it before all the nuggets are gone eat all the nuggets the number of minutes it takes to eat all the nights and there you go we have everything you always wanted to know about eating nuggets write students exponential functions 35 the change in the population of fruit flies can be modeled by the equation T is equal to 302.75 ^ T where T is time and days write a statement to describe the change in population of fruit flies so we the population of fruit flies is is it increasing or decreasing to answer that you look at the parentheses if it is greater than 1 then its increasing if it is less than 1 and it is decreasing .75 is less than one there for decreasing and by what percent So within your parentheses is always going to be plus or minus if it's are decreasing and your are is the percent rate so to find what the r is which is what this question is asking you will track .75 from one when I do that we get point to 5.25 is the decimal representation of the percent in order to get the purse you will move your decimal 2 places right and put a % so this is decreasing by 25% a question 36 the equator f of x is equal to 50 on to 1.1 power of X shows with C 1.1 is greater than 1 so it is increasing and by what percent this time we're going to subtract 1 from the 1.1 and I'm going to add another decimal place because usually that's what we had there which would give us 1 0 to make that a percent we move decimal 2 places can we put a percent so this would be by 10% 37 word problem mrs. Robbins is behind on grading papers the number of assignments she has to grade is growing exponentially by 25% the equation is given to you you do not have to write it yourself how many assignments will she have to grade after 8 days we are simply plugging in 8 for the X phone so it would be like a half of 8 is equal to 120 on 21.25 ^ 8 you take your calculator you put your calculator just like that we are raising 1.25 ^ 8 before we * the hundred and twenty and we can't 700 and 15 assignment bearded 38 graph and make a table for y is equal to 16 on 2 1 / 2x ^ x + this is another problem that you use your calculator for so we are going to put two sooner go into the Y equals screen and put the just like that in there and we've we look at the table we are going to have going to start at -1 and this would be a 32 because we put a -1 in 4X and put that all in your calculator you get a 32-0 would give us a 16-1 would give us eight two would give us four three would be to 4 would be one 5 would be .5 so let's see about rapping that we are just going you're just going to five right and then let's go up by twos here okay so the 16 here in the equation is our starting point right that's our Y intercept so it's going look like this course you can you can plot these you can also look at the graph on your calculator 3 2 snowboarding the corporate for 1 it's just barely above the zero so this is what it looks like there we go all right alright writing exponential functions Miss White number 39 this white begin the year drinking 7 Cups of Tea a day that amount increased I-10 percent what's our starting point write an equation for the amount of Cups F of team is white will drink after 30 weeks so put T is equal to P represents our starting point what we had at the very beginning it's increasing so it's plus here and 10% we will ride as a decimal we always have its above the whole number to decimal is here we go to places left so it's Point 1 or 1 0 and we have tea and I want to put that together just to make it a little later we have a 50 is equal to 7 + 1 + 1 would be 1.1 and we had he is our exponent all right that's 39 40 says Aladdin's Magic Carpet is worth $200 after Jasmine spilled soda on it it's value decreased 8% every months write an exponential function to represent the situation and then we are evaluating what the carpet will be worth after six months preg so let's ride the equation excuse me we have f of x and the initial values 202 that goes in for the p and 1 minus the 8% now 8% we move our decimal still two places so that decimal is .08 so we have one - 08 and we just have X here and let's put that together then so 1 - 08 is going to be .92 and then we are evaluating it for six months and it increased by every month so six goes here a six goes here and you almost used you have to use a higher calculator that has an exponent key so at least a scientific calculator if you're doing this at home to get these exponents right so this is we use our calculator to do that than once again we're raising this to the power and then multiplying by the 200 not the other way around your you have to use your order of operations in this is going to be 121 dollars and twenty-seven cents patterns and graphing sequences number 42 graphing ordered pairs for the sequence given by the formula a sub in equals 8 + 2 on 2 N -1 by looking at the equation that it's arithmetic and we know that 8 is the first term the common difference is going to be at 2 so let's make 5 ordered pairs and plot these now what is sequences we're going to start with one isn't Sierra we start with one so if I put a 1 in 4000 * 220 + so I get an eighth really already knew that it was paid because that's the first term goes in the equation 2 - 1 is 111 * 2 is to 2 + 8 is 10 I put a 3in 4in 3 - 1 is 2 * 2 is 44 + 8 is 12 which is what the equation told us would happen so I know that 4 is going to be 14 and 5 is going to be 16 so let's plot those on our graph when our x-axis we are just incremental I once and there's no reason to go more than 5 but on the y-axis of believe we need to go up by twos okay and let's parties 1/8 go right there 210 so it looks like these are just going up by ones but since our scale is going up by 2 it's really what's happening we called this a discrete graph because a sequence a sequence is not connected so we're going to leave those just like that and there we have grabbed our arithmetic sequence graph the ordered pairs for the sequence given by this formula now one clue we have is that instead of an we have a g we also have multiplication year 3 * 2 to the exponent of n -1 so we know this is geometric so it is not going to Whittier this one so let's look at the ordered pairs we generate for when I plug in here so if I put a one-in-four in in the exponent one line is 102 to the 0 power is 105 x 3 3/4 we also knew the first term was going to be at 3 from just looking at the equation write 2 and 4 in to -1 is 1 1 ^ ^ 1 is 2 2 * 3 is 6 putting 3 and 4 in train 14 and would be 3 - 1 is to 2 squared is for 4 * 3 is 12 so it's increasing a little faster in this one of four in four in four minus 1 is 3 2 to the 3rd power 2 * 2 is 424088 * 3 is 24 right and stop there because I don't think we can fit anymore on our grasp at once again let's increment the x-axis by once this time we're going to go up by fours that this is important that you have uniforms schedule here you can't number your Y axis 360 12:24 because that is not a uniform scale we need to go up by fours 2482 1620 2428 32 I guess that's it's about all we need to Let's Play 1 and 1/3 would be about right there to 6 312 right on that one 424 so I guess at that point we see that it is not linear right it is not a linear function it is exponential that's what it which way should look it's a curve it is not aligned and I don't know what that is okay there we have it okay now we have number 44 given the sequence 5 8 11 Etc determine if the sequence is arithmetic or geometric okay so you start and you can subtract your terms and see if we're the same answer to 8 - 5 is 311 - 8 is also 3 so with this is the same number it is arithmetic and the common ratio or difference ratio means it's associated with a geometric difference meaning subtracting is this arithmetic and the common difference then is the three identify the next term in the sequence will that would be 11 + 3 because it's an increasing sequence and that would be 14 so I put a 14 and then you're asked to write the explicit explicit formula so let's we're going to call it a sub in a sub in and then we start with the first term the where the first term is 5 what's the common difference which is 3 and in parentheses in minus one this says we can get every term by taking the previous term and multiply it by three minutes after we added to the first time so that's 44 now 45 if we start and stop tract 15 - 100 or 100 - 50 and it is a decreasing this is going to be 50 but if I say 15 - 25 I get a totally different number so at this point I can rule out an arithmetic sequence so let's see about a geometric sequence in to determine if it's geometric sequence you divide so if I say 50 divided by 100 and that's going to reduce 5/10 to be 1/2 and if I did say 25 / 50 I can divide both of those by 5 or actually I can divide both by 25 and I also get 1/2 Saudi determines that the sequence is geometric now the common ratio or difference it is a ratio it is a decreasing decreasing sequence so we cannot say well we're dividing by two every time because it has to be in terms of multiplication so what we are multiplying by is the one hat 100 * 1 is 5050 * 1/2 is 25 so we are riding 1/2 or point five identify the next term in the sequence well 25 time 1/2 is 12 1/2 and then writing the explicit formula all right we're going to go with a G this time we still start with the first term pictures of hundred but we're not adding this time we're multiplying this time and inside the parentheses is our common ratio well I'm going to put it is 5 you can write 1/2 if you wish and the exponent always going to be in minus one is part of the exponent and we're done okay students we are almost finished with this yet so let's look at the last standard writing sequence rules 148 find the 15th term in the sequence ASAP in equals 3 - 2 on 2 N -1 now it's because of the format of this we know that it's arithmetic and we know that threes the first term and the common difference is not a to but so that means that our sequence is going to be decreasing so when it says 15th term we just substitute 15 and 4 in do we have 3 - 2 on 2 15-1 15-1 is 14 and 14 * 2 is 28 so this would be 3 - 20 which would be a -25 that is a razor 49 says I have four teddy bears on a day on day one we're starting a sequence Monday 2 I have 80 Monday 3 I have a hundred how many teddy bears will I have on day 6 okay there two ways to do this weekend write the explicit and what is happening well we are doubling each time so it's going to be a geometric sequence the 5 right can explicit formula I had the first term which is 40 we're doubling that means my common ratio is and then if we are putting a 6 there well sorry in - 1 week what it is six 4 in six mile 20 is 5 2 to the 5th power 2 * 2 is 4240828 * 16 to * 16 is 30 to 2 * 32 is 64 so that's 40 * 64 and that is 1280 Sarah Wright scripture about the 64 from let me check myself two to the fifth power is no that's not right at all 32 40 x 32 now that looks right okay but the other way to do it is to just continue on our sequence until we get to the 6th term that would be if I double 160 that's going to be 3:20 a double 320 that's 640 that's fifth term and then 640 * 2 would be 1280 so two ways to do it either one alright I'm proud of you for enduring through all of this and I hope it makes it a little more clear you're going to do great on your midterm

Uploaded by Teri Windham.

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5/6/19 Midterm Study Guide Instructional video

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