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November 08, 2025, 05:13:18 am
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Author Topic: Variable rates of change  (Read 905 times)  Share 

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mandy

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Variable rates of change
« on: June 29, 2009, 04:41:54 pm »
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A swimming pool is being emptied and the amount of water remaining in the pool t minutes after emptying commences is given in the table below.
time (min)  0          20       40        60      80
volume (L) 30000  28800  25200  19200  10800
a. Find the equation describing the volume of water remaining at any time.
V=30000-3t2

b. Find the rate at which the pool is being emptied.

Im not sure what I should be doing here.
I tried to find the gradient, but that didnt work.
The correct answer to b is 300L/min.

Thank you :)
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TrueTears

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Re: Variable rates of change
« Reply #1 on: June 29, 2009, 04:49:16 pm »
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b) The rate at which the pool is empty is denoted by

300L/min corresponds to the rate at which the pool is emptied when t = 50 mins.
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mandy

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Re: Variable rates of change
« Reply #2 on: June 29, 2009, 04:53:31 pm »
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Thanks, but how do I know that I should pick t=50mins ?
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TrueTears

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Re: Variable rates of change
« Reply #3 on: June 29, 2009, 04:55:09 pm »
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The question should ask you that, ie, "Find the rate at which the pool is emptied when t = 50"

If it just says "Find the rate at which the pool is being emptied" then it is simply in terms of t.
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mandy

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Re: Variable rates of change
« Reply #4 on: June 29, 2009, 04:58:14 pm »
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Oh wait, I know. Its because I typed the question wrong. The question should read:

Find the average rate at which the pool is being emptied.

Sorry, does that change anything ?
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TrueTears

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Re: Variable rates of change
« Reply #5 on: June 29, 2009, 05:00:01 pm »
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Quote from: mandy on June 29, 2009, 04:58:14 pm
Oh wait, I know. Its because I typed the question wrong. The question should read:

Find the average rate at which the pool is being emptied.

Sorry, does that change anything ?
lol, yes that changes it all.

consider average:
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mandy

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Re: Variable rates of change
« Reply #6 on: June 29, 2009, 05:04:44 pm »
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Where's the -6 from?
Is it the rate of change (gradient)?
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TrueTears

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Re: Variable rates of change
« Reply #7 on: June 29, 2009, 05:06:39 pm »
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denotes the instantaneous rate at which the water is emptied.



You are given 4 values of t.

You need to find the average.

Hence my working.
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mandy

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Re: Variable rates of change
« Reply #8 on: June 29, 2009, 05:09:44 pm »
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Okay, thanks heaps :D
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