Question

Suppose that the demand function for a product is given by D(p)=65,000/p​ and that the price p is a function of time given by p=2.1t+9, where t is in days. Find the demand as a function of time t. b) Find the rate of change of the quantity demanded when t=80 days.

Answer 1

To find demand as a function of time, substitute the price function into the demand function for D(t). To find the rate of change of the quantity demanded at t=80 days, differentiate the demand function with respect to time and evaluate at t=80.

Step-by-step explanation:

The student has asked how to find the demand as a function of time, given that the demand function for a product is D(p) = 65,000/p and the price p is a function of time defined by p = 2.1t + 9. To answer this, we substitute the price function into the demand function to get D(t) = 65,000 / (2.1t + 9). This gives us the demand as a function of time.

For part b), to find the rate of change of the quantity demanded when t = 80 days, we differentiate the demand function D(t) with respect to time t to find D'(t), and then we evaluate D'(t) at t = 80 days. To do this:

1. Differentiate D(t) = 65,000 / (2.1t + 9) with respect to t to find D'(t).
2. Substitute t = 80 into the derived function D'(t) to find the rate of change at that particular time.