Good morning from\u00a0Jack, your tutor from Campbell River.\u00a0 It’s brilliantly sunny here, with a high of 27 (or 81 F) expected.\u00a0 This kind of weather can be so hard for kids just returning to school.<\/p>\n
The people entering math 12 will probably encounter exponential growth very soon.\u00a0 It’s not a term you hear very often, but compound interest is an example of it.\u00a0 Most natural things grow the same way – while they have the resources.<\/p>\n
Exponential growth means that the growth is a percentage of how much is already there.\u00a0 So if your growth rate is 10%, then you go from 10 to 11 in one year.\u00a0 If you start with 100, though, you go to 110 in that year.\u00a0 Interest is the obvious example:\u00a0 everyone knows that if you have $1000 on deposit, you’ll get more interest than if you’ve only got $100.<\/p>\n
Step two is the one that surprises some people.\u00a0 Let’s imagine you start with 1000 individuals at 10% growth.\u00a0 At the end of year one, you’ve got 1100 – true enough.\u00a0 The mistake many people make is that they assume that the following year, the population increases by another hundred, making 1200.\u00a0 That’s not true.\u00a0 If you start the second year with 1100, still at 10% growth, the population will increase that year by 110 – which, of course, is 10% of 1100.\u00a0 So by the end of year two, you’ll have 1210:<\/p>\n
1000 + 100=1100\u00a0 (100 is 10% of 1000).<\/p>\n
1100 + 110=1210\u00a0 (110 is 10% of 1100).<\/p>\n
The difference is only 10 at the end of year two, but that difference keeps getting larger because it contributes to the growth of the population.\u00a0 That’s why, believe it or not, the population will be over 2000 in less than 8 years.\u00a0 In 32 years it’ll be over 21 000.<\/p>\n
The rule of 72 for compound interest says that<\/p>\n
(interest rate)x(doubling time)=72<\/strong><\/p>\n (Of course, that law is an approximation, but actually a very good one.)<\/p>\n Since compound interest is just an example of exponential growth, that law works for anything that\u00a0grows exponentially.<\/p>\n Enjoy this beautiful day.<\/p>\n