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

In summary, the problem involves finding the rate of increase (in cm/s) at the time when the radius of a circular ink spot has doubled from its initial value. The formula for the radius at time t is r=\frac{1+4t}{2+t}. After analyzing the problem and checking the calculations, the rate of increase is 9/7cm/s, not 7/9cm/s as originally thought.
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The radius of a circular ink spot, t seconds after it first appears, is given by:

[tex]r=\frac{1+4t}{2+t}[/tex]

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?
 

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  • #2
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.
 

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