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2002 Paper 2 Q4b) - HSN forum

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2002 Paper 2 Q4b)


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#1 celticfcz

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Posted 12 May 2007 - 03:19 PM

Hey all was just going through my past papers and found that I am not understanding part b of this question:

4. A man decides to plant a number of fast-growing trees as a boundary between his property and the property of his next door neighbour. He has been warned, however, by the local garden centre that, during any year, the trees are expected to increase in height by 0.5 metres. In response to this warning he decides to trim 20% off the height of the trees at the start of any year.

(a) If he adopts the "20% pruning policy", to what height will he expect the trees to grow in the long run?

(b) His neighbour is concerned that the trees are growing at an alarming rate and wants assurances that the trees will grow no taller than 2 metres. What is the minimum percentage that the trees will need to be trimmed each year so as to meet this condition?

In part (a) the only thing I could see to do was find the limit which I did and got 2.5 - which was the correct answer. Im just stuck on b) and wondering if anyone could explain this?

Thanks wink.gif

#2 babeasc

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Posted 12 May 2007 - 04:22 PM

Right, I get this...

Growth per year = 0.5
Amount left after trimming = 80% = 0.8

U(n+1) = 0.8Un + 0.5

Since -1<0.8<1, a limit exists



\begin{align*}L &= \frac{b}{1-a} \\ &=\frac{0.5}{(1-0.8)} \\ &=\frac{0.5}{0.2} \\ &= 2.5\end{align*}

Just looking, i think B is just the limit formula again, but trying to find a?



\begin{align*}L &=\frac{b}{1-a} \\ 2&=\frac{0.5}{(1-a)}\end{align*}

therefore



\begin{align*}(1-a)&=\frac{0.5}{2} \\ &=0.25 \\ -a&=0.25-1 \\ -a &= -0.75 \\ a &= 0.75\end{align*}

75% ?

Is that the right answer? Can't see any other way to do it...
Beyond it, and us, shines a greater hope and a brighter future
Can't wait 'til the exams are over!

#3 celticfcz

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Posted 12 May 2007 - 04:25 PM

The answer is 25% - maybe just the difference?

thanks

#4 babeasc

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Posted 12 May 2007 - 04:34 PM

Auch silly me!

I was figuring out 'a', which is whats left lol

So yeah, if theres 75% left, then it needs to be cut by 25%

Yay!

x
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#5 celticfcz

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Posted 12 May 2007 - 04:41 PM

Thanks a lot I finally get it!! Didnt even have a clue where to start.

Thanks again!





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