Monod Growth Model The Monod growth curve is given by f (x) = cx k + x for x 0, where c

Chapter 5, Problem 7

(choose chapter or problem)

Monod Growth Model The Monod growth curve is given by f (x) = cx k + x for x 0, where c and k are positive constants. The equation can be used to describe the specific growth rate of a species as a function of a resource level x. (a) Show that y = c is a horizontal asymptote for x . The constant c is called the . (b) Show that f (x), x 0, is strictly increasing and concave down. Explain why this implies that the saturation value is equal to the maximal specific growth rate. (c) Show that if x = k, then f (x) is equal to half the saturation value. (For this reason, the constant k is called the .) (d) Sketch a graph of f (x) for k = 2 and c = 5, clearly marking the saturation value and the half-saturation constant. Compare this graph with one where k = 3 and c = 5. (e) Without graphing the three curves, explain how you can use the saturation value and the half-saturation constant to decide quickly that 10x 3 + x > 10x 5 + x > 8x 5 + x for x 0.