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12 replies to this topic

#1 jword

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Posted 22 March 2008 - 11:37 PM

During its first year a species of tree reaches a height of 7cm. It continues to grow for another 9 years attaining its maximum height at 10 years of age. Each year it continues to grow at the rate of double the previous years height. At what age will the tree be half its maximum height?
Spoiling for answers....
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#2 brhan

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Posted 22 March 2008 - 11:58 PM

During its first year a species of tree reaches a height of 7cm. It continues to grow for another 9 years attaining its maximum height at 10 years of age. Each year it continues to grow at the rate of double the previous years height. At what age will the tree be half its maximum height?
Spoiling for answers....

Spoiler for my guess

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#3 Noct

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Posted 23 March 2008 - 12:16 AM

Spoiler for ...

Edited by Noct, 23 March 2008 - 12:22 AM.

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#4 itachi-san

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Posted 23 March 2008 - 01:26 AM

Spoiler for answer

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#5 Noct

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Posted 23 March 2008 - 03:40 AM

Spoiler for ..

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#6 bonanova

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Posted 23 March 2008 - 03:49 AM

During its first year a species of tree reaches a height of 7cm. It continues to grow for another 9 years attaining its maximum height at 10 years of age. Each year it continues to grow at the rate of double the previous years height. At what age will the tree be half its maximum height?
Spoiling for answers....

Spoiler for Looks like...

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#7 Noct

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Posted 23 March 2008 - 04:31 AM

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It is not the only reasonable alternative.
How i understood it, and what i contend is the most reasonable interpretation, is that each year it grows double it's height at the beginning of the year. Therefore it would triple its height each year.
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#8 bonanova

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Posted 23 March 2008 - 05:35 AM

It is not the only reasonable alternative.
How i understood it, and what i contend is the most reasonable interpretation, is that each year it grows double it's height at the beginning of the year. Therefore it would triple its height each year.

Hi Noct,

My comment was not meant to say your answer is wrong.

I was commenting, rather, about the OP:

First, I would say it's not a well posed problem.
Consider the significant differences among these three statements.

[1] Each year it continues to grow at the rate of double the previous years height.
[2] Each year its height changes by a multiplicative factor equal in magnitude to two times the current height of the tree expressed in cm.
[3] Each year its height increases by an amount equal to two times its current height.

Statement [1] is from the OP and is not well posed.
Statement [2] is well posed, and would be, to my thinking, what the OP tried to say.
Statement [3] is well posed and leads to your answer.

If you take the OP as a formula for calculating next year's growth rate from this year's height:
[1] leaves you in the dark as to what units to use: cm, inches, feet, meters and furlongs all give different results.
[2] works, but isn't what the OP says.
[3] tells you how the height changes, but it isn't what the OP says; it doesn't address growth rate at all - rather a growth amount.

Second, a growth rate most commonly refers to the derivative of height with respect to time, and it has the units of [length]/[time].
If [2] is what is meant, calling a factor a rate is incorrect; they have different dimensions. Rate is dimensionless.
If [3] is what is meant, calling a height increase a rate is also incorrect. Summarizing,
Rate = [length/time]; height and height increase = [length] and factor = [dimensionless].
To say Rate = 2 x Height creates a dimensionality error.
To say Factor = 2 x Height also creates a dimensionality error.
To say Height increase = 2 x Height is dimensionally correct, but the OP purports to specify a rate.

So to my mind the OP does not say clearly how the tree grows.

Regarding my comment about alternative, I'm simply saying that if you abandon the idea of calculating a growth rate [or factor or height increase] from the tree's current height, you're pretty much left with taking the OP to say that the height, itself, doubles each year.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#9 chanakyavg

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Posted 23 March 2008 - 06:49 AM

Nice Q. It reminded me of a problem I got in my 9th grade 22 years ago, by my teacher to check if I was paying any attention. :) wow I am old.

What is product of :

(x - a) (x - b) ........ (x - z) ?

The question itself has a loop hole. If we pay attention to this question, it doubles every year and grows for 10 years, then when is it 1/2 the height. Well throw people off, we could have mentioned 22 years and still would have come up with the answer (22 - 1 ) years.

Nice brain teaser.
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#10 storm

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Posted 23 March 2008 - 06:54 AM

YOU TRIED TO POSE A TRICK PUZZLE>>>WHICH TURNED UP INTO A ......
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