 Okay, here we go. Population increases at 4.8% annually. It's a population. This is an exponential growth equation, so I'm going to write this down. And I'm going to list my data. Let's see. I think C, if it's increasing at 4.8%, is going to be 1.048. Annually, that's telling me my growth period. My growth period is every one year. They didn't tell me my final and initial. Well, they did. They want the population to triple. I think I'm going to let my final population be 3, and my initial population be 1. Or you could let the final be 6, and the initial be 2, or the final be 3 million, and the initial be 1 million. But regardless, I always pick the simplest one, Jimmy. My equation is going to look like this. 3 equals 1 bracket 1.048, and T is what they're asking me to find. And it's T over 1. Am I going to write T over 1? No. Is this one going to make any difference, either? Okay. T is sitting up there. I'm going to take the log of both sides, and the T would move to the front. In fact, I'm going to get this. T equals the log of 3 divided by the log of 1.048. It says, give your answer to 2 decimal places, if necessary. Clear, clear, clear. Log 3 divided by the log of 1.048, 23.43, yeah, 23.43. If you got that 2 out of 2, otherwise I would probably give you half mark if I saw that, half mark if I saw that, half mark if I saw that, and a half mark for the answer. Does it matter what? I won't be fussy on units in math 12. Physics 12, yes. Math 12, no. Although, you still should. I won't take marks off, if that's what you're asking. Does it matter? Yes, absolutely, because you should always include units. Will you cost you marks? Call me in physics. That's a better answer to your question. Half-life question, okay, so we're still going to go with A equals A0C to the T over P, but as soon as it's a half-life question, by definition the growth rate is 0.5. Oh, and they've told me the half-life, it's 3.2 days, that's the half-life. How many days? T is what they're asking me to find, I think A0 is 246, I think the final amount is 50. I think the equation is going to look like this, 50 equals 246.5 to the T over 3.2. I'm going to divide by 246 right now. What I cannot do is go 246 times 0.5, oh, that's half of 246, so there's an exponent on here and now, don't do that. Unfortunately, if you do that, I'll give you a half mark for the equation and then I've got to stop marking because everything else after that is garbage. Don't do that. Please don't do that. I'm going to write 0.203 but I'll use this answer, the complete answer. I'm not going to round off, 0.203 equals 0.5 to the T over 3.2. Take the log of both sides, the log of 0.203 equals T over 3.2 log 0.5 and move the fraction to the front as a great big fraction. I think T is going to end up being 3.2 times the log of 0.203 divided by the log of 0.5. I think T is going to end up being 3.2 times the log of answer button divided by the log of 0.5. You get 7.36, people nodding, 7.36. I would give you a half mark if I saw that, a half mark if I saw that, a half mark if I saw that and a half mark for the answer. Find the half life of this, oh, half life. This time they're asking me to find the half life. They're asking me to find P. That means T is 90, it's a half life question so C by definition is 0.5, initial amount is 250, final amount is 50, it's going to look like this, 50 equals 250.5 to the 90 over P. I am not going to go 250 times 0.5, no, no. I'm going to divide by 250. When I go 50 divided by 250, I think this one works out a little nicer. You get exactly 0.2 equals 0.5 to the 90 over P. Take the log of both sides and move the exponent to the front. This is over 1, cross multiply, I think you're going to get P equals 90 log 0.5 divided by log 0.2 when all is said and done. I think you're going to get P equals, no idea, 90 log 0.5 divided by log 0.2. You get 38.76, 38.76, spread, days, days, whatever. Once again, half mark if I saw that, a half mark if I saw that, a half mark if I saw that, and a half mark for the answer. Turn the page. Now we're doing compound interest. I did say this question was a bonus question. They want the final amount. The equation is going to look like this. The final amount equals the initial amount, 1 plus 0.08 divided by compounded quarterly to the power of 9 divided by one quarter is your growth period. By the way, 9 divided by one quarter, that's really 36, which is what I'm going to type. I can just go straight to my calculator here, Hailey, because A is on ground level, A is going to be 600 times 1 plus 0.08 divided by 4 close bracket to the power of 36, 9 over a quarter. You get $1,325.93, 1, 3, 2, 5, 90, say what was it, 3, half mark. Number five. How many times stronger is an earthquake in South America, Richter scale 7.3 compared to an earthquake in Asia, Richter scale 5.6? It's going to be 10 to the 7.3 minus 5.6 equals how many times stronger. Now here's your hint. On your test, I'm not going to ask you to find this. On your test, I guarantee you a SAR. I'm going to tell you this and ask you to find one of those. One of those would be an exponent, which means I'll have to take the log of both. Oh, cool. That's why it fits into this. But here, this one's a little bit easier. It's going to be 10 to the power of what is 7.3 minus 5.6. I should have done that in my head, but gosh, I can't believe I typed that in. 1.7. Try that again, Mr. Duk with a decimal. 5.88. 5. Wow. Good gosh, Mr. Duk. Hit that button. 50.12 times as strong. 50 times stronger, basically is what we would say on the news. And the last one. Population is described with the following equation. What's the initial population? Hopefully, you all got that. 340,000. What's the growth rate? 5.5%. Rewrite this as a continuous growth rate. Now, I made this worth one mark because this is a tough topic. It should be worth two marks in terms of the amount of work. I didn't want to hammer you guys. So, what they're really saying is rewrite A to the K as 1.055. Place the 1.055 with E to some power because that's not going to change and the T's not going to change. The only thing that's changing is we're replacing an E to the K with that. What they're really saying is find the growth constant. How will I do that? I won't take the log of both sides. What will I do instead? Ln both sides. ln of E to the K equals ln of 1.055 and that moves to the front. I get K ln of E equals ln of 1.055. Wonderfully, the ln of E is just 1. I get K equals ln of 1.055. Now, if you want 0.05, because technically that's to do decimal places, that's fine. Usually, for an exponent, I'll try and carry four decimal places because rounding off an exponent has way more significance. It has exponential growth significance. So, I usually carry exponents to four or more decimal places. So, I'm going to write this, 0.0535. Now, they want me to rewrite the above equation. Okay. That's really your final answer. That's what I would like to see for the half mark. If you found that, that gets you a half mark as well. And, once you have done that, if you can give yourself a lovely, wonderful score at the top of the page, not out of 11, but I guess out of 10, because number four was a bonus. And yes, you can get 11 out of 10. Yep. And making sure your names are on them, pass them inwards and then we'll move on to the next quiz. All right. Quiz six. More half-life slash exponential growth type questions. Oh yeah. In fact, this wants me to find the half-life. So, A equals A0C to the T over P. So, I know that C equals 0.5. I know that A0 is 600. I know that final amount is 125. They better tell me T. Oh yeah, 30. P equals, don't know. 125 equals 600.5 to the 30 over P. I'm going to divide by 600. I am not going to go 600 times 0.5. 125 divided by 600. I'm going to write 0.208, but I'm going to use 0.20833. I'm going to use my answer button. 0.208 equals 0.5 to the 30 over P. And now I'm going to take the log of both sides. Is that right? And I think I'm going to get this. P equals 30 log of 0.5 divided by the log of 0.208, which is 30 log of 0.5 divided by the log of my previous answer. I'll use the whole thing. You get 13.2 three decimal places this time. 13.257. Ah, this one's worth three marks, which is probably what it will be on your test, because then I can go one, two, three, four, five lines. Perfect. I can even say a half mark if you remember the equation. A half mark for plugging it in. A half mark for that. A half mark for that. A half mark for that. And a half mark for the answer. I totally watched that little circle there. A certain substance to define the half life. Okay. A equals A0C to the T over P. 200 equals 750.5 to the 10 over P. Sorry? It froze? Oh, thank you. Patience while it figures it out. Wireless is now disconnected. On my screen that just appeared. So now I plug in again, and we have wireless is now reconnected. Should beep, should flip, and I should be back in about three, two, one. I'm back. Time to sort it. There we go. I'm not going to go 750 times that. I'm going to divide. 200 divided by 750. 200 divided by 750 is 0.26 repeating. I'll write 0.267, but I'll carry that decimal. Take the log of both sides. P is going to end up being 10 log 0.5 divided by the log of 0.267. 10 log 0.5 divided by the log of that answer there. You all get 5.244. Half life is 5.244 days. And I'd probably go with the same marking scheme. A half mark for that. A half mark for that. A half mark for that. A half mark for that. A half mark for that. And a half mark for your final answer. What that really means, by the way, is if you just write down an answer, you get half out of three, which suggests I'm trying to emphasize the process. I hope. Example three. Ooh, now they want me to find k. How do I know this is base e? Because there's an e right there. And I said to you, Brett, if I do give you a base e question, Joel, I'll give you the equation as well. Although, can you see it's really, really similar to the one that we've memorized anyways? We're going to get this. 150 is my final amount. 992.9 is my initial amount. E to the 9k. T is 9. I don't want to write k times 9. I'll write 9k, because that's how we're seeing it. I'm going to divide both sides by 992.9. And I'll get 0.151, blah, blah, blah. I'll write 0.151. 0.151. 0.151 equals e to the 9k. I'll take the ln of both sides. And when I do that, the 9k will move to the front. Thankfully, Tyler, the ln of e is 1. Hard to get the k by itself, Tyler. Darn right, I would. k equals the ln of 0.151 divided by 9. The ln of that answer divided by 9. Do you get negative point? Does it say what to... I'll go to 2 to... I guess negative 0.21? Yeah, I guess no matter what I round off to, it's going to be negative 0.21 unless I go to 7 decimal places. What's the negative telling me? We're decaying. We're losing matter. For what it's worth. Three marks. One, two, three, four, five. Oh, I'd probably go... A half. A half. A half. A half. And then one whole mark for the answer. Turn the page. I had some people wondering about these. So here is your if then questions. Base A, base A, base A. I'm not base changing. I'll break this puppy up. This is going to be the log of x cubed minus the log of y. And I wrote the square root as an exponent right away. I said square root, that's a one half power. Why did that help? Because I can move the exponents to the front. Why did that help? Turns out the log of x, it says, is 0.6. And the log of y, it says, is 3.8. In fact, this ends up being 1.8 plus... So I can do the math in my head. Plus, Mr. Duick. You can do that in your head. Nice try. Shut up. Minus. Nobody noticed. Half of y... Is it 1.8 minus 1.9? Is it negative 0.01? Not 0.01. Negative 0.1? Apparently, I can't do the math in my head. And I would probably go something like this. Half mark if I saw you break it up. Half mark if I saw you move the exponents to the front. A half mark if I saw you do that. Make the substitution. And then a half mark for the answer. And you know what? 5 and 6 are going to be almost identical. Different numbers, but it's going to be a really, really similar procedure. I'm going to say, hey, this is really... Because I know it's all base A again. This is going to be log base A of x to the 1 half minus the log base A of y squared. Which is going to be 1 half log base A of x minus 2 log base A of y. Which is going to be a half of 0.2 minus 2 times 2.8. Which I'm pretty sure is 0.1 minus 28 times 2 is 5.6. Is the answer negative 5.5? Half mark, half mark, half mark, half mark. Number 6, log base A of x equals 0.08. You know what? It's the same thing. The log base A of x to the fourth minus the log base A of y to the 1 fifth. Because fifth root is 1 fifth power. 4 times 0.8 minus 1 fifth of 9.8. Okay, this one I'll go to my calculator. It's got some decimals. I mean 4 times 0.8 is 3.2. But the other one I'll be paranoid on. 4 times 0.8 minus 1 fifth times 9.8. You get 1.24? There you go. Half mark, half mark, half mark, half mark. Give yourself a lovely score on this quiz. Out of count them. 15 please. So can you open your books please to page 201? Page 201. Page 201. Last day, page 201. Last day we looked at compound interest. We said it was exponential growth disguised just a little bit. But I'll start out by saying hey any questions from here you want me to go over. Now is your chance to ask. Really you had to tweak the interest rate. If they gave you the interest rate Carly for the entire year you had to recognize oh. 12% for a whole year compounded quarterly means take the 12 and divide it how much for a quarter of your divided by 4. Or compounded semi-annually divided by 2. Or compounded monthly divided by 12. Or compounded daily divided by 365. And you had to recognize that your period was either a quarter or a 12th or a half or 1,365. Any of these? Okay can you all get out then your great big huge log review this one here. There are some questions I'm going to tell you to nuke. Pardon me? Um sure I guess although you could always have just brought it. Just be thinking. If you don't have it you want to write this down somewhere. Everybody else find it please. Hand it out at the very beginning of the unit. There it is. These are questions I think you can nuke. So so far I've circled a few. It was quite a while ago I assigned some. As of right now they're all going to be fair game. I'm going to put a star next to number six. Number six is nasty. I would consider number six an A or A plus level question. Doesn't mean you can nuke it but don't think there's like 40 of these on your test. Maybe one if that. Okay. You can nuke number eight. I guarantee you number nine is on your test. I'll even be more specific than that. Number nine will be the first question on your test. Or I'll give you something as an exponent and say write it as a log. But I'm telling you right now remember your test has two parts. A non-calculator section and a calculator section. The first question on the non-calculator section is going to be hey can you rewrite something as a log or as an exponent? There was a few I wanted to nuke here. Thought there was. I'm getting there. Hey Mr. Dewick. You said you're going to nuke some questions. I know I did. I know there was one I wanted to nuke. I thought there was. Bear with me. It might be on the written section. There's a lot of these Mr. Dewick. Well, I'm giving you lots of practice. That's good. That's good. That's good. That's good. Oh yeah. 66 is overkill. 66. Well gee thanks Mr. Dewick. One whole question. Shut up. That's good. That's good. That's good. That's good. That's good. Radioactive. Good. Good. Good. Find the domain. Should be running out of questions soon Mr. Dewick. That's good. That's good. You can nuke number 101. Don't do me any favors. Okay. You can nuke on the written section. Number four. Yeah. Those are the four questions that you can ignore. And very last thing. This is what I call the unit two review quiz. This actually used to be my test. It's what I gave out for years. And then about six years ago, the government added a non-calculator section to the provincial site to split my test up, so I re-typed it. So this is all one, but you can kind of think about which questions you wouldn't need a calculator for, or which questions would. This will take you a good chunk of time. This is what we're going to be marking the first thing on Wednesday. Okay. When's your test? Monday? When's your tutorial? Right now, I'm looking at going, I think Thursday after school. Because I have a feeling if I went Friday after school, most of you would be going, I can do it Friday after school. If you guys think more of you want to come, we'll vote. Who would prefer Thursday after school? One, two, three, four. Who would prefer Friday after school? Okay. So right now the Fridays have it. The only reason I wanted to give me an extra day was, sometimes it's nice to have an extra day to ask questions after the questions, but whatever. Okay. So Friday after school it is. The button for punishment, am I? That's okay. How long will it go? As long as it lasts, probably till 4.30, maybe till 5. Maybe shorter. But I'll stay until people are content. Okay. The remainder of the class is yours to work on the great big take home quiz and also start working on the big review. And please remember the answer key to the big review is online. Before you ask me, look online so you can figure it out yourself because you'll have learned it better.