Bone mass In Example 1.1.6 we found an expression for the mass m of a human femur of length L in terms of the outer radius r, the inner radius rin, and their ratio k − rinyr. More generally, if the bone density is , measured in gycm3, then bone mass is given by the equation m − r 2Lf 2 s 2 1dk2g It may happen that both  and k change with age, t.

(a) If  changes during aging, find an expression for the rate of change of m with respect to t.

(b) If k changes during aging, find an expression for the rate of change of m with respect to t.