Calculate the Rate of Increase for Doubling Radius of an Ink Spot

[Procrastinate]

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

$$r=\frac{1+4t}{2+t}$$

Find the rate of increase (in cm/s) at the time when th radius as doubled from its initial value.



I have attached my working; however, the answer is 7/9cm/s and I keep getting 9/7cm/s. Does that even make sense if it is doubling anyways?

 

[hgfalling]

I don't see any problem with your work; it seems to me that 9/7 is right. 7/9 is the rate of change at t=1, but that doesn't correspond to the condition given in the problem, since the initial radius is 1/2 and the radius at t = 1 is 5/3.