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Hello, and welcome to another episode on growth and decay.

This is lesson four of eight, repeated percentage change.

I just want to start by saying hope we've got the pen and paper we can write stuff down with, and I hope we've got a calculator ready as well.

It's really important, we're going to do loads and loads of stuff to do with calculators so we really need that calculator, specifically a scientific one that we can really focus in on and use to the best of our ability.

Make sure you're in that quiet space, that room that you need in order to concentrate as much as possible.

Make sure your phone has the apps nice and silenced like mine does currently.

I've got it away and I've got it completely turned off so we can really concentrate and I'm not going to be disturbed.

So without further ado, I'm Mr Thomas, let's take this lesson away.

So for our try this, what I'd like us to consider is that Yasmin buys a guitar for £80 After a year, it has gone up in value by 10%, after another year it's gone down by 10%.

So I've then got her saying, "I think it's worth more than £80." I've also got Xavier saying, "It increased in value, "then decreased in value by the same amount, "so it's now worth £80 again." Can you justify both their responses? Or think of maybe why they're right or wrong.

So pause the video now, do that task please for eight minutes, off you go.

Very good, let's come back to it then.

So let's analyse what's actually happened.

What's happened is we've paid £80 for that guitar and it's gone up by 10%.

So what we're going to have to do is 80 multiplied by 1.

10.

And that of course gives us £88.

So at this point here, this is going to be £88, but then we're told that it goes down in value by 10%.

So what happens at this point is we've got 88 multiplied by 0.

9.

And if we type that into our calculator, well, what do we get? We get £79.

20.

That's really strange, isn't it? So the reason being is because we've gone from £80 up to £88, which is a 10% increase, but then remember we've got that 10% extra, right? And then we're having to do 10% of that, so we're getting actually 1% lower than we originally started, if you can see that.

So it now is worth £79.

20.

So you can see why it may be worth £80 again because you're doing 10% then decreasing by 10%.

Cancels out, right? It doesn't, so it's really important to be aware of that.

So Yasmin is thinking it's worth more than £80 is totally wrong.

It's definitely going to be, it's worth less, and then she'd be correct, yeah? So that provides response to this.

So for our connect today, we're going to consider that in a bit of a wider context now.

I'm going to say £100, if it grew by 5% and then another 5%, is it the same as growing by 10%? Well, let's try it.

If we had £100 multiplied by 1.

05, you'd then have to multiply it by 1.

05 again.

And if you notice, if you've got the same number there multiplied, you can square it.

So it's going to be £100 multiplied by 1.

05 to the power of two.

And that of course is equal to, if we chuck that into our calculator, we get £110.

25.

Is that the same as growing by 10%? Well, £100 growing by 10% would mean we need to multiply it by 1.

10, which of course is equal to £110 and zero pence.

So they're clearly not equal.

So we can say a resounding no, of course not, just to really highlight the point there, lovely.

So we can clearly see that they're not equal, right? It's because of that what we call compounding effect, that's sort of the increase upon the increase, yeah? What about if you had £500? Is that the same if it was increased by 50% and then decreased by 50%? Is it still £500? Well, let's check it out.

If we did that, it would be £500 multiplied by 1.

5, and that gives us £750.

We then need to decrease it by 50%.

So I can take that £750, there we go, times it by 0.

5, so 1/2 it, and what do I get if I get half of 750, that will be, 1/2 of 750, can you beat me to it? I'm still thinking, I'm still thinking, it's going to be £375 pounds, isn't it? Good stuff.

So we can see it actually after all that, it definitely is not £500.

That 375 is not equal to the £500 there.

So therefore we can say that of course it's not the same.

So with that in mind and what we've learned so far, I'd really like you to have a go at doing the independent task.

I'm going to give you 12 minutes now to have a think about what to do there because there are some quite weird questions there so I really want you to make sure you're getting it.

So take 12 minutes now, pause the video and have a go at that task please.

So here are the answers for your independent task.

We can clearly see here, we've got 5% followed by another 5%, so it's going to be 1.

05 times 1.

05, and that's the same as 1.

05 times, sorry, to the power of two.

What about this one? Well, we can clearly see 1.

4% for three years means that we're going to have to do 1.

014 multiplied by 1.

014 multiplied by 1.

014, which gives us 1.

014 to the power of three, three years hence to the power of three, or cubed.

So it's really important you can see that.

We're going to discuss that in a later episode, a later lesson, but for now bear that in the back of your mind because that's really important.

What about this one then where we see a 13% decrease, 0.

87, that one there, and then the 35% increase there, 1.

35, and that would be £1.

17 to the nearest penny.

Then what about the multiplier? Well, we're doing 1.

07 to the power of five, five years, 7% increase, this part here, and then the five years just there.

That would give us, well, my calculator told me that it was going to be that, so just be aware that there could be a few more decimal places, but I've rounded it there, okay? Fingers crossed you've got all that and we can move on.

So for your explore today, what I'd like you to do is I'd like you to consider how we could fill in the blanks to make the final box as great as possible, so biggest number possible, as small as possible, and as close to 80 as possible.

So have a go at that task now.

I'm going to give you, oh, how long should I give you? I'm going to give you 15 minutes to have a go at that because I think some of it might be a little bit tricky.

So pause the video now and have a go at that, please.

Okay, excellent, let's go on then.

So we've got as great as possible, well, we want to minimise the amount that we are getting rid of at first, right? So we'd want 10%, which would take us down to 72, so we can tick that one off.

We'd then want to probably do 30%, so 30% of 72.

So in order to make it as great as possible, what I could do is I could do an increase that's very big.

So 90% increase, and a 90% increase with multiplied by 1.

9, which of course would give us 152.

Then we want to minimise that, the decreased part there.

So we want to do 10%, and 10% would be 15.

2.

So you can subtract that from the amount we've got there.

So that would of course give us 136.

8.

So I've used the 10%, I've used the 90%.

Then I need to increase it by the biggest amount possible, so 70%, that would give me, times by 1.

7, 232.

56.

And then I can decrease it by a small amount, 30%.

So increase it by 30% would give me 1.

3, multiplying it, so 302.

328.

And then decrease it by 50%, so what I'm left with is 151.

164.

So we've done now as great as possible.

As small as possible is going to be essentially just the opposite of what we've done.

So if I want to do as small as possible, what I'm going to get is, I'll do this in blue this time, to decrease it, you want to get as low as possible, so 90%, right? Oh, my apologies, that's increasing.

We want to increase it by a very small amount, so 10%.

So if I increase by 10%, I'm going to get 88, decrease it now by a very large amount, so 90%.

So 90% of that would be, decreasing it by 90% would give us 8.

8 because we're only left with 10% of course.

So then from there, we then need to increase it by a small amount, so 30%.

So I can then multiply it by 1.

3, that gives me 11.

44.

I can then multiply 11.

44 by a very, very substantial decrease, so 70%.

So I need to do 0.

3, and that gives me of course 3.

432, and then I can increase it by 50%.

So times that by 1.

5 and I get 5.

148.

So we can see we've used them all there, and we've gone from 80 all the way down to 5.

48.

So there's a very big decrease in the grand scheme of things, that's as small as possible we've got.

I'm going to leave as close to 80 down to you because that's going to be a lot of playing around and you're going to see, you could probably get quite close, but I'll leave that one to you.

So that brings us the end of the lesson.

I just want to say very, very big congratulations to you at home for doing so well.

And I just want to say that's a really tricky topic in some respects.

So if you've kept up and you've tried as hard as you can, you've got most of those answers correct, that's really, really good work, well done.

Prove it to me and everyone else in the exit quiz, and make sure you can get full marks, five out of five, that'd be fantastic.

For now though, take care, and I shall see you in the next episode, buh-bye.