Question

For the demand equation, find the rate of change of price p with respect to quantity q What is the rate of change for the indicated value of q ? p=e−0.0034,q=50 The rate of change of price p with respect to quantity q when q=50 is (Round to five decimal places as needed.)

Answer 1

The rate of change of price p with respect to quantity q when q=50 is approximately -0.00176.

Step-by-step explanation:

The rate of change of price p with respect to quantity q can be found by taking the derivative of the demand equation with respect to q. Let's differentiate the equation, p = e^(-0.0034q), with respect to q:

dp/dq = -0.0034e^(-0.0034q)

Now we can substitute the given value of q = 50 into the derivative equation:

dp/dq = -0.0034e^(-0.0034*50)

Using a calculator, we can calculate the value of dp/dq as approximately -0.0017620065. Therefore, the rate of change of price p with respect to quantity q when q = 50 is approximately -0.00176.