Project

Differential Equations

(Business and Economics)

1. Total Profit from Marginal Profit:

A firm's marginal profit P as a function of its total cost C is given by

.

(a) Find the profit function P(C) if P = $10 when C = $16.

(b) At what cost will the firm break even?

2. Stock growth:

The growth rate of a certain stock is modeled by

where V = value of the stock, per share, after time t (in months), L = $24.81, the limiting value of the stock, and k = a constant. Find the solution to the differential equation in terms of t and k.

3. Utility:

The reaction R in pleasure units by a consumer receiving S units of a product can be modeled by the differential equation

.

where k is a positive number.

(a) Use separation of variables to solve the differential equation.

(b) Rewrite the solution in terms of the initial condition R (0) = 0.

(c) Explain why the condition R (0) = 0 is reasonable.