Rath on 15 June 2008
Alright, I'm studying for a maths exam on monday and this question has me completely stumped.
Essentially its a seperation of variables question and it involves the equation
ds/dt=k(a-s)
Where 'a' is the initial value and the initial value is 50.
From what I have worked out this is
1/(50-s)ds = kdt
-ln(50-s) = kt
ln(50-s) = -kt
50-s = e^-kt
s = 50 - e^kt
However the correct answer is apparently s = 50(1 - e^kt) and I can't figure out how on earth they got that. Be very useful if somebody can help me out here.
Essentially its a seperation of variables question and it involves the equation
ds/dt=k(a-s)
Where 'a' is the initial value and the initial value is 50.
From what I have worked out this is
1/(50-s)ds = kdt
-ln(50-s) = kt
ln(50-s) = -kt
50-s = e^-kt
s = 50 - e^kt
However the correct answer is apparently s = 50(1 - e^kt) and I can't figure out how on earth they got that. Be very useful if somebody can help me out here.
