Also I'd like to ask another question related to this. If you've got this equation:
dR/dt = 0.4R
and you integrate it.
dR/R = 0.4 dt
ln(R) = 0.4t + c
R(t) = ke^0.4t (k = e^c)
Now lets just say I start with a 8 R's:
So dR/dt = 0.4(8)
(1) R = 8 + 3.2 = 11.2
Now if I plug the same values into R(t):
k = 8
t = 0
R(t) = 8e^0.4(0) = 8
I get 8 which seems correct.
now If I put t = 1, I get:
R(t) = 8e^0.4(1) = 11.9346 (4 d.p)
Now according to my (1) I should get 11.2 not 11.9346. Why is this?
Also I'd like to know why R(t) = k(1.4)^t works?
From what I understand, R(t) = ke^0.4t is the solution, not R(t) = k(1.4)^t.
Can someone please help me with this. I'm very lost