Question

(Please help!) One way to describe the concentration of an acid is as a percent by volume. For example, in 40 mL of a 30% acid solution, the volume of pure acid is 40 x 30/100 or 12 mL, and the volume of water is 40-12 or 28 mL. If 5 mL of pure acid is mixed with 20 mL of water to give 25 mL of acid solution, the concentration of the solution is given by 5/25 x 100% = 20 %. If water is mixed with 50 mL of 40% acid solution, write an equation that describe the acid concentration, C(x), as a function of the volume of water added, x.

Answer 1

The answer is C(x) = (20/50 + x)*100% and I have to graph C(x) versus x. But how do I graph it on the graphing calculator?

Answer 2

The answer on the back of the book is:

Answer 3

If that's the answer, then just graph this :

C(x) = (20/50 + x)

forget about the 100% because 100% = 1

Answer 4

but on my graphing calculator it's a diagonal line.. o.o

Answer 5

it's still a diagonal squiggly line.. o.o

Answer 6

Are you sure you have posted the proper function?

Answer 7

ohh.. I plot that on my graph and yes I posted the proper function D:

Answer 8

Then why are there negative numbers associated with it? Something has to be wrong

Answer 9

Okay so the function of the volume of water added, x is: \[C(x) = 20/50 + x \times 100\]

Answer 10

*100%

Answer 11

Your function isn't clear enough because it could be interpreted in two different ways

Answer 12

oh boy. D:

So with one of the two ways, what function will have the same graph as i drew above?

Answer 13

\[C(x) = \frac{20}{50} + x \times 100\] or \[C(x) = \frac{20}{50+x} \times 100\]

Answer 14

And I forgot the percent sign.

Answer 15

ohh.. it shows from the back of my book the second function..

Answer 16

idk, there is something about the function you must be misinterpreting

Answer 17

in the question above, what function would you get?

Answer 18

Okay, well in that case, it is :

\[C(x) = \frac{2000}{50+x}\]

Answer 19

Graph that and tell me what you get

Answer 20

I get a diagonal line.. o.o

Answer 21

The something is wrong with your calc or you're just not graphing correctly

Answer 22

how do I graph it correctly?

Answer 23

Enter this exactly:

2000/(50+x)

Answer 24

If you have 50 ml of 40% acid, you have a constant amount of acid and that is 20 ml
So the acid fraction as you add water is 20/(50+x)

Answer 25

I didn't even bother to calculate the acid fraction because she said the answer was in the back

Answer 26

If you get a diagonal this time, check to see if you are set to radian (not degree) mode

Answer 27

There's nothing shown on the graph.. o.o

Answer 28

You're probably in degree mode. switch back to radians

Answer 29

but It's on radians :(

Answer 30

What kind of calculator do you have ?