Differential Equation

The rate at which weight is lost by an animal suffering from a viral infection is observed to satisfy the relationship \displaystyle \frac{dy}{dx} = \frac{t}{72}\left(8-t\right)^{\frac{1}{3}} for 0 \leq t \leq 8.  Here L is the weight loose, as a percentage of the animals original weight, t weeks from the time of infection.  Find the function giving the percentage weight loss L at time t, and determine the percentage weight loss when the animal dies eight weeks later.

Source: Rosenberg, R.L. (1984). Elementary Calculus: Course Notes. Ottawa, Canada: Holt, Rinehart and Winston. (Exercise 44: Question 3, p. 132)