C3 differentiation

Hi,

I got the right answer with this question, but only by messing around with it and not really understanding the logic behind what I was doing. Could anyone explain why what I did gave the correct answer..it really doesn't make sense to me.

The radius, r cm, of a circular ink spot, t seconds, after it first appears, is given by:

r=$\frac{1+4t}{2+t}$ The initial size is found by letting t=0.

Calculate the time taken for the radius to double its initial size.

So, initially I thought to double the RHS as the radius has doubled. But that was wrong. Then, just messing a little, I let r=1 and then found t. t=1/3, which is correct. But how so? There is nothing to indicate that r was 0.5. I'm not sure of the logic....could anyone explain? Thanks!

Hi,

I got the right answer with this question, but only by messing around with it and not really understanding the logic behind what I was doing. Could anyone explain why what I did gave the correct answer..it really doesn't make sense to me.

The radius, r cm, of a circular ink spot, t seconds, after it first appears, is given by:

r=$\frac{1+4t}{2+t}$ The initial size is found by letting t=0.

Calculate the time taken for the radius to double its initial size.

So, initially I thought to double the RHS as the radius has doubled. But that was wrong. Then, just messing a little, I let r=1 and then found t. t=1/3, which is correct. But how so? There is nothing to indicate that r was 0.5. I'm not sure of the logic....could anyone explain? Thanks!