Question

Initial Value Problem:

dA/ dt = 6A,,,,,,,,,,,,,, A(0) = 9,

Solve for A(t) = ????

Answer 1

@ganeshie8

Answer 2

@satellite73

Answer 3

@hartnn

Answer 4

separate out the variables,

keep terms with A on one side and t on other side of =

Answer 5

I did that already,

I got to the point where I have dA/dt = 6 dt

after integrating you will get ln(a) = 6t.

Am I right so far?

Answer 6

add the constant of integration!

ln A = 6t +C

Answer 7

now you can use the fact that

A(0) = 9

do you know what that means ?>

Answer 8

I know but ln(0) is undefined,,,, this is where I got stuck.

Answer 9

that means, its not clear to you :)

A(0) = 9
means

when
\(\Large t=0, A=9\)

Answer 10

Oh okay, so now we solve for C. Thanks a lot, I know that but had a long. Thanks again.

Answer 11

welcome ^_^

Answer 12

@hartnn One more question. After you solve for C, how do you seperate A as a function?

Answer 13

ln(A) = 6t + ln(9)

Answer 14

you want to isolate A ?

Answer 15

I want A(t) = something.

Answer 16

yep, that means you need to isolate A

Answer 17

bring ln 9 on left side
and use log property

ln x - ln y = ln (x/y)

Answer 18

ln(A/6) = 6t?

Answer 19

ln(A/9) = 6t

yes

Answer 20

now again if you're good with logs, you shouldn't have any problems
\(\Large \ln a=b \implies a=e^b\)

Answer 21

so A/9 = e^(6t) ?

Answer 22

@hartnn I got it thanks!!!!! I really appreciate your effort.

Answer 23

welcome :)