## Recurrence relations :S

### Azie

Posted 20 October 2007 - 07:14 PM

I think ive dun these questions hundreds of times an now i dnt even no which way is right ...please help! xxxx

Q1. The sum of £1000 is placed in an investment acccount on January 1st and thereafter £100 is placed in the account on the first day of each month. Interest at the rate of 0.5% per month is credited to the account on the last day of each month but the interest is calculated on the amount in the account on the first day of the month.
(a) how much is in the account on june 30th?
(b) on wat day does the account first exceed £2000?

For this question, ive got the notation 2 b: Un+1 = 1.05Un + 100, U0 = 1000 ??

Q2. Each evening, park rangers manage to clear 85% of the litter dropped in the park during the day. Approximately 2kg of litter is dropped daily
(a) if there is 4kg of litter in the park just before cleaning on Monday evening, how much litter will there b after cleaning on Thursday?
(b) if this trend continues, how much litter will there b in the park?

For this queston, ive got the notation 2 b: Un+1 = 0.15Un + 2, U0 = 4 ??

### xClairex

Posted 20 October 2007 - 07:34 PM

QUOTE(Azie @ Oct 20 2007, 08:14 PM)
Q2. Each evening, park rangers manage to clear 85% of the litter dropped in the park during the day. Approximately 2kg of litter is dropped daily
(a) if there is 4kg of litter in the park just before cleaning on Monday evening, how much litter will there b after cleaning on Thursday?
(b) if this trend continues, how much litter will there b in the park?

For this queston, ive got the notation 2 b: Un+1 = 0.15Un + 2, U0 = 4 ??

u1=amount of rubbish after the park was cleaned on monday night
u2-tuesday night
u3-wednesday night
u4-thursday

the formula for un+1 is right so use that to work out:u1,u2,u3,u4.

b)work out the limit limit=b/1-a

hope this has helped you if it still makes no sense then i will show you how to work it out

### Azie

Posted 20 October 2007 - 07:45 PM

I worked it out like that initially but my answer for U4 was the same as the limit so i wasnt sure then if i had dun it right.

U0 = 4
U1 = (0.15 x 4) + 2 = 2.6
U2 = (0.15 x 2.6) + 2= 2.39
U3 = (0.15 x 2.39) + 2 = 2.36
U4 = (0.15 x 2.36) + 2 = 2.35

L = 0.15L + 2
L - 0.15L = 2
0.85L = 2
L = 2 / 0.85
L = 2.35

### Steve

Posted 21 October 2007 - 11:46 AM

Yes, this can happen - the limit may be a term in the sequence.

### Azie

Posted 21 October 2007 - 12:44 PM

ahh ok, that makes sense ...thanks a lot

### Azie

Posted 21 October 2007 - 05:10 PM

Any input on the 1st question? xxxx