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)

= 3.2

(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