Chapter 9, Problem 21E

The transport of a substance across a capillary wall in lung physiology has been modeled by the differential equation

$\frac{dh}{dt}=-\frac{R}{V}\left(\frac{h}{k+h}\right)$

where h is the hormone concentration in the bloodstream, t is time, R is the maximum transport rate, V is the volume of the capillary, and k is a positive constant that measures the affinity between the hormones and the enzymes that assist the process. Solve this differential equation to find a relationship between h and t.