Videos

4-12 AIM3 8.3 Tables of Exponential Functions

Added Apr 12, 2024 •

Copy this URL:
Embed code:	<iframe class="edlio-embed-player" type="text/html" width="640" height="360" src="//www.pointlomahigh.com/apps/embed/?v=371981" frameborder="0" allowfullscreen></iframe> Change dimensions

Show Transcript

all right let's continue our conversations exponential functions today is a couple of things you'll see before you recursive definition for a certain situation we'd like to another way of writing that and also will be interested in if you're given a table can you create an exponential function just based on that table but before we do that I think proper Frost remind ourselves just what an exponential function so you might want to pause and write down the definition all right so I hope you wrote 8 * y equals f of x equals 8 oz be Jackson what what's true about these are you sure will a can't be zero be got to be positive but it can't be equal one and one more things remember the Dome well that's all real values he was going on here we got the van okay maybe this is a balanced situation if you have $500 in the bank in your earning 6% interest of pretty good what's going to happen down the road if let's say we can you track of years you just definition to calculate via 10 how to get on your calculator we could put that in our calculator a couple different ways one ways we could start at 500 * 106 get whatever * 2.106 by the way your calculator if you do something like say for example I don't know 3 * 2 and it says 6 then press X to again it'll say answer times to get 12 but now if you just push enter it knows you want * 2 + start automatically doubling that's a nice way of doing repeated multiplication ever comes up so we could do that here start with the 500 * 1.06 and eventually get to be of 10 but before we do the second part about a more direct way rather how to clean all the intermediate would be nice just to go there I got a little sore for you can you rewrite this using sequential notation it we learned earlier so as always I'm going to ask you to pause while you're right out and then I will I will reveal it to you okay well I hope if you had to go back and look things up we did and let's see where we go we started at 0 our rule is 1.06 * 2 previous value and our first outfit was 500 yes everything seemed so great all right let's go into the other question that one more direct way to get to be attend rather than doing 500500 * 1.069 * 1.06 again who do we write it rather than in cursive could we ride it enclosed form I thought with mulch by the same thing over and over that's what's Happening Here be the X you keep multiplying by B whatever you got to say when X is 1 when X is too it's just me another multiplier be so what do we have going on here what we're starting at 5 100 and it would * 1.060 is 1.06. She had said at the end so I should do it to the end so if I want fee of ten I can do 500 * 1.06 and I'll have it by the way these two functions are not the same I mean the recursive and the the clothes warm here this is what we called from the definition of how we create this is discrete the only search for certain values mainly starting at zero and creasing buy one this function really wouldn't exist for be of let's say 1.3 but over here in what's essentially a continuous function I'm Puttin any value and so they certainly would agree for all the integer values 0 1 2 3 chetra but this function couldn't find me of 1.5 where is this one could that's an important difference and depending on what you doing you might for one than the other alright let me ask you another Pop Quiz this function that we've created here is it gross or is it the cake well I hope this 1.06 told you something it's getting bigger * 500 * 1 and a little bit more so I must be getting bigger so the must be a growth function let's look at a different situation is off to a new type of problem to hear some here's a table it's all the way take a look at that table what do you notice growth so that's nice that make sure I can see but clearly things are getting the output to getting smaller so this is decay that how is it we can tell from a toy what you doing with an exponential function hope your memory kicks in you might look all you doubt he probably build a quotient column or ratio called and to test it you would take any out divided by the one before it and let's see if I can squeeze this in here so 50 / 100 out that's a half then he ride have twenty-five divided 50 and a half and I won't bother with the next 16.25 / 12.5 do since these are the same ye just tells me it's exponential and in fact I could say that this function and close form without its starting at 100 Andy rate of change * 1/2 so we have 100 * 1/2 to the x so then there's my clothes form could you and by that I mean to do it now right recursive Okay so hope you had the output is 100 for our initial input of 0 and for every value better that what happened it got half as large the 1/2 time L of H minus one that is the previous so it's not looking to spend more kind of situation on the next page find a rule that fits this table review of things you've discussed in previous classes one of the first test you ever learned was perhaps it's linear but maybe I should jump up jump back for what kind of test have you done over the last few years what kind of functions have you been able to determine if a table could possibly be well I hope you said linear quadratic and from this year lagrange's interpolation and of course now we're talkin about exponential let's go back true outlander's and that might number we took a look at the first difference well 12:00 and 6 I just 1818 and 9 up there not the same okay so these are not the same so we know it's not linear just to go in my little order the next thing I think we're going to check is quadratic and for that you will call with a second difference now in this case unfortunately we can't get to a second differences we don't have enough let's just pretend we have and they were all three okay so they're all three that tells us is quadratic I know we need to buy for my nerve cells a x squared plus BX plus City well what would a b remember if these are all the same in the egg is the second difference / 2 that means a would-be trehab and Steve the y-intercept that's free so she's obviously 12 the question is how do we find B the one approach of courses we could just plug in a and C then we could pick any of these points to be accent f of x then we could just simplified and figure out what he is going to be fine but I wonder if she remembers shortcut that you've met previously there it is the Lord yourself if you did remember that A + B is equal the first difference is starting at 0 so in this case hey we already know it's 3/2 so 3/2 + B would have to equal the first difference which is fixed and so 1612 have that would be be is 9/2 until we could say that possibly the rule is f of x equals that was a 3/2 so all I was called 1.51 point five x squared + 9/2 + 4.5 x + C 12 we could test and see if that works I suspect it will hologram I still remember how we did the garage I'm not going to go through the whole thing but you might recall that we start by creating this type of Express first I would ignore the 27 x - throw in an extra minus one with an unknown coefficient then I have zero into and then I would have one and two and then we would say well fm0 is 12 + plug it in I let X be 0 this time this time of drop out and work out hopefully your memories kicking in and so we would discover turns out we get these values and this would create another function that could describe the table we have here but James for Tomball Texas peninsulas let's look at exponential approach remember that the run ratio from this case and that would give us a 18/12 which is your do sit 3/2 or 1.5 if you want and if I do what's next over 18 it also reduces the three over to say hey fantastic and this this is the bee value night with half of x equals a x b e to the X and this is the bee value remember that doesn't look like bvx does it B to the X Number One X is zero the zeros one you get the a value we have that for free day is 12 so now we know we could describe it as f of x equals 12 times 3/2 or 1.5 to the X until we have these different oceans all which contain these three points I can make a probably pretty bad gas but I'll give it a shot, let's see here do the quadratic minnoco should I say that's 12 and so it looks yes and then the exponential here while it awfully goes to 12 and then the other can do something something like this was going to come up I am out there that's that's too bad I'm not trying to make you no pictures will come up same intercept and then for a little bit it's actually inside and then the what a mess I'm making it make it a little bit prettier exponential outside there for a bit and then eventually comes back inside and then they go off an ingrown you could look into some business if you wanted not the clearest picture in the world so we can start on the key what we're after if you have a table you know represent how can you find the function that I would ask you to look on page 603 read the minds and actions and then show you a couple different methods which one do you prefer they're both fine and maybe times perhaps think one is more appropriate in certain situations another I'll leave that up to you to think about you should be familiar with both alright take it

Uploaded by Brian Macky.

Videos

4-12 AIM3 8.3 Tables of Exponential Functions

More videos from Brian Macky