I get the graph for part (a) (i) but could someone explain part (ii) and (b)?

## 2003 paper II question 11

### Mr H

Posted 19 May 2005 - 07:56 AM

Here's a solution: http://www.mathsroom.co.uk/hsnposts/2003_P2_Q11.pdf

(It is 114kb so may take a few moments to download depending on your connection)

(It is 114kb so may take a few moments to download depending on your connection)

### tupacshakur

Posted 19 May 2005 - 10:08 AM

hmm that solution doesnt make any sense to me

how do you get a.a(^x) = a(^x) + 1 from a(^x+1) = a(^x) + 1

how do you get a.a(^x) = a(^x) + 1 from a(^x+1) = a(^x) + 1

### tupacshakur

Posted 19 May 2005 - 04:46 PM

i still dont have a clue whats going on. Hopefuly this wont come up 2moro.

### Dave

Posted 19 May 2005 - 04:56 PM

why does a

well lets use numbers

3

what is that the same as.....well 3x3 or 3

the exponent is a way of showing you the number of times the number has been multiplied by itself.

so if you had x

which is the same as multiplying x "n" number of times then multiplying by "n" 1 one time

^{x+1}= a.a^{x}well lets use numbers

3

^{2}= 9what is that the same as.....well 3x3 or 3

^{1}x^{1}the exponent is a way of showing you the number of times the number has been multiplied by itself.

so if you had x

^{n+1}that is saying x has been multiplied by itself n+1 timeswhich is the same as multiplying x "n" number of times then multiplying by "n" 1 one time

### dfx

Posted 19 May 2005 - 08:53 PM

See..

a ^(x +1) can be expanded into a^x multiplied by a^1

Remember your laws of exponents? When you multiply two numbers with powers and the same base, the powers get added right? Like 2^4 * 2^5 = 2 ^ (4 + 5 ) = 2^9

SO, to get a.a^x, you just do the above procedure in REVERSE. Which means a ^ (x + 1) = a^ x * a ^1 < try multiplying this out, and you get a ^ ( x + 1 ), see?

SO, now that we know in expanded form its a ^ x * a ^ 1

BUT, a^1 is just a. so that makes a * a^x = a.a^x

a ^(x +1) can be expanded into a^x multiplied by a^1

Remember your laws of exponents? When you multiply two numbers with powers and the same base, the powers get added right? Like 2^4 * 2^5 = 2 ^ (4 + 5 ) = 2^9

SO, to get a.a^x, you just do the above procedure in REVERSE. Which means a ^ (x + 1) = a^ x * a ^1 < try multiplying this out, and you get a ^ ( x + 1 ), see?

SO, now that we know in expanded form its a ^ x * a ^ 1

BUT, a^1 is just a. so that makes a * a^x = a.a^x