Question

Calculus Help?

Answer 1

@zepdrix @Kainui
@Loser66

Answer 2

Sup?
Figure out part a?

Answer 3

Nope XD

Answer 4

\[\large\rm \frac{dy}{dx}=(500-y)\]"multiply" dx,\[\large\rm dy=(500-y)dx\]And divide the other stuff, ya?

Answer 5

\[\large\rm \frac{dy}{500-y}=dx\]

Answer 6

ok so that is our separation.

Answer 7

ya, now integrate and do some stuff

Answer 8

integrate, algebrate, solvebrate :)
all the fun stuff

Answer 9

so just int the separation equation?

Answer 10

mhm

Answer 11

-ln|500-y|=x+C

Answer 12

and then find the constant (C) by subing in y(0)=7

Answer 13

C=-6.2

Answer 14

Hmm they would like to see the general solution.
I don't know if they mean in terms of x, or if they want you to leave it like that.. hmm

Answer 15

Oh oh oh,
I suppose if you're solving for C at this point,
then yes you end up with a weird value for C.
Better keep it as an exact value, no decimal.

Answer 16

well for c it says to solve for the constant so C=-6.2

Answer 17

Well its -6.20051

Answer 18

\(\large\rm C=-ln(493)\)

Answer 19

Exact value^

Answer 20

so leave it like that?

Answer 21

Yes.
If you use the decimal value, it's going to mess up your final answer probably :p

Answer 22

After we plug that value in,\[\large\rm -\ln|500-y|=x-\ln(493)\]Solve for y to get your particular solution.

Answer 23

oh ok so then for d it would just be x=-ln|493|-ln|500-y|

Answer 24

You solved for x,
I said solve for y.

Answer 25

how do i take the variable out of the abso value i cant remember...

Answer 26

Ummm, you don't really have to worry about that so much.
Did you deal with getting it out the log yet?

Answer 27

x=log(493/(|500-y|))

Answer 28

Again, you solved for x... lol

Answer 29

oh crap i forgot we are solving for y XD

Answer 30

y=500−e^x/493,500+e^x/493

Answer 31

y=500+-e^x/493

Answer 32

Hmmm

Answer 33

\[\large\rm -\ln|500-y|=x+C\]Lemme show you how I would proceed from here.

Answer 34

wait i forgot the - beforee the first ln

Answer 35

y=500+-493/e^x

Answer 36

Ah ok nevermind my steps then :)
That looks better.

y(0)=7 will only satisfy the positive or negative case,
figure out which one.

Answer 37

It's negative :)

Answer 38

\(\large\rm y(x)=500-493e^{-x}\)

Ok yay good job \c:/