Question

Write and solve the differential equation that models the verbal statement. (Use k for the constant of proportionality.)
The rate of change of y is proportional to y. When x = 0, y = 10, and when x = 2, y = 25. What is the value of y when x = 4?

Answer 1

dy/dt=ky

Answer 2

dy/dx = ky

y = ??



Evaluate the solution at the specified value of the independent variable.
y = ??

Answer 3

wait
dy/dx=ky

Answer 4

\[\frac{dy}{y}=kdx\]

Answer 5

Integrate both sides:
\[\int{\frac{dy}{y}=\int k*dx}\]

Answer 6

\[ln|y|=kx+C\]

Answer 7

I think it's going ot be 25 =10e^k(2)

Answer 8

x = 0, y = 10
ln|10|=C
\[ln|y|=kx+ln10\]

Answer 9

\[e^{ln|y|}=e^{kx}*e^{ln10}\]
\[y=10e^{kx}\]

Answer 10

x=2, y=25
25=10*e^(2k)
2.5=e^(2k)
ln(2.5)=2k
k=ln(2.5)/2

Answer 11

\[\large{y=10*e^{\frac{ln2.5}{2}x}}\]

Answer 12

And to figure out what's y when x=4:
y=10*e^(2*ln(2.5)), just use a calculator
Hopefully I didn't make any silly mistakes

Answer 13

nope :).

Answer 14

Yay

Answer 15

62.5 yay!

Answer 16

lol when u said nope, I thought the answer didn't wrong... then i saw the smiley and got relieved hahah

Answer 17

20 more to go!

Answer 18

OMG

Answer 19

jk :P

Answer 20

Btw I have my own hw lol, I wasn't planning on sticking around. Still have to submit this stupid excel project, write a physics lab, and 2 programs. I have no idea why I'm wasting time here.

Answer 21

Got a handful :P. These are the toughes! I'm good in Physics, and what kinds of programs? :P

Answer 22

C++

Answer 23

oh yeah you were doing the c++ stuffs.

Answer 24

still fighting your teacher about the negating spaces? :P

Answer 25

I know it, it's just tedious... and very boring, and no, I gave up on her.. she can't teach at all

Answer 26

sux, I learned on my own....

Answer 27

lol I learned with a diff professor, I was retaking the same course basically

Answer 28

Lots of bad professors out there... That's why I did it all on my own... You learn much more than the classroom can teach you...