Dam problem

A

Aza

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May 5, 2019
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Hey guys, I am really stuck on this, if anyone could make sense of this it would be fantastic.
Here is the question:

A reservoir contains 600 kilolitres of water at 5.5% acidity. The capacity of the reservoir is 2 megalitres.
Water with an acidity of 3% is entering in to this reservoir at a rate of 8 kilolitres per hour.

After 10 hours:
i) How much water is in the dam? ( I did a simple table and found that 680 kilolitres would be in the dam after 10 hours?)

ii) How much acid is in the dam? (I did a simple table and found that 35.4 kilolitres of acid would be in the dam after 10 hours?)

b) Define variables and write an equation for:

i) The volume of water in the reservoir as a function of time, v(t) ( I answered: f(t)=v+t*8 Where v is 600 in Kilolitres of water, t is the time in hours and 8 is the constant being added per hour of the tank being filled.) - This seems to work against the table I made in the graph I did.

ii) The amount of acid in the reservoir as a function of time, a(t) ( I answered: f(t)=a+t*0.24 Where a is 33 in Kilolitres of acid, t is the time in hours and 0.24 is the constant being added per hour of the tank being filled.) - I think this is wrong because I can't get the graph to work for this..

c) Combine these formulae in (b) to express the percentage of acid in the reservoir as a function of time. Why is this a rational function? -

And there are 5 more questions detailing range, asymptotes and intercepts and some other stuff but I won't put them here..
 
Aza said:
Hey guys, I am really stuck on this, if anyone could make sense of this it would be fantastic.
Here is the question:

A reservoir contains 600 kilolitres of water at 5.5% acidity. The capacity of the reservoir is 2 megalitres.
Water with an acidity of 3% is entering in to this reservoir at a rate of 8 kilolitres per hour.

After 10 hours:
i) How much water is in the dam? ( I did a simple table and found that 680 kilolitres would be in the dam after 10 hours?)

ii) How much acid is in the dam? (I did a simple table and found that 35.4 kilolitres of acid would be in the dam after 10 hours?)

b) Define variables and write an equation for:

i) The volume of water in the reservoir as a function of time, v(t) ( I answered: f(t)=v+t*8 Where v is 600 in Kilolitres of water, t is the time in hours and 8 is the constant being added per hour of the tank being filled.) - This seems to work against the table I made in the graph I did.

ii) The amount of acid in the reservoir as a function of time, a(t) ( I answered: f(t)=a+t*0.24 Where a is 33 in Kilolitres of acid, t is the time in hours and 0.24 is the constant being added per hour of the tank being filled.) - I think this is wrong because I can't get the graph to work for this..

c) Combine these formulae in (b) to express the percentage of acid in the reservoir as a function of time. Why is this a rational function? -

And there are 5 more questions detailing range, asymptotes and intercepts and some other stuff but I won't put them here..
Click to expand...
Your work in part (i) and (ii) are correct.

I do not quite understand your statement - "I can't get the graph to work for this". Please explain how do you come to this conclusion.

Please share your work regarding part (c). If you are stuck with part (c) - please tell us where you are confused!
 
Thanks, yes, I see the graph works for the part b (ii) now, I was looking at it wrong.
I can't combine the functions to get an appropriate percentage on the graph, I don't even know if I am doing it right, I tried f(t)= 600+t*8/33+t*0.24..
Is this how I combine the two or am I doing something wrong?
 
Aza said:
Hey guys, I am really stuck on this, if anyone could make sense of this it would be fantastic.
Here is the question:

A reservoir contains 600 kilolitres of water at 5.5% acidity. The capacity of the reservoir is 2 megalitres.
Water with an acidity of 3% is entering in to this reservoir at a rate of 8 kilolitres per hour.

After 10 hours:
i) How much water is in the dam? ( I did a simple table and found that 680 kilolitres would be in the dam after 10 hours?)

ii) How much acid is in the dam? (I did a simple table and found that 35.4 kilolitres of acid would be in the dam after 10 hours?)

b) Define variables and write an equation for:

i) The volume of water in the reservoir as a function of time, v(t) ( I answered: f(t)=v+t*8 Where v is 600 in Kilolitres of water, t is the time in hours and 8 is the constant being added per hour of the tank being filled.) - This seems to work against the table I made in the graph I did.

ii) The amount of acid in the reservoir as a function of time, a(t) ( I answered: f(t)=a+t*0.24 Where a is 33 in Kilolitres of acid, t is the time in hours and 0.24 is the constant being added per hour of the tank being filled.) - I think this is wrong because I can't get the graph to work for this..

c) Combine these formulae in (b) to express the percentage of acid in the reservoir as a function of time. Why is this a rational function? -

And there are 5 more questions detailing range, asymptotes and intercepts and some other stuff but I won't put them here..
Click to expand...
\(\displaystyle the \ percentage \ of \ acid \ in \ the \ reservoir \ = \ \dfrac{The \ amount \ of \ acid \ in \ the \ reservoir \ as \ a \ function \ of \ time}{The \ volume \ of \ water \ in \ the \ reservoir \ as \ a \ function \ of \ time} \ * 100 % \)
 
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