Question

If the cost C (in dollars) of removing p percent of the particulate pollution frem the exhaust gases at an industrial site is given by the equation shown below. C(rho)=100−rho9100p​ Find the rate of change of C with respect to rho. c′(p)=

Answer 1

The rate of change of C with respect to rho can be found by taking the derivative of the cost function C(rho). The derivative of C(rho) with respect to rho is -1/9100p.

Step-by-step explanation:

The rate of change of C with respect to ρ can be found by taking the derivative of the cost function C(ρ) with respect to ρ. The given cost function is C(ρ) = 100 - ρ / (9100p).

To find the derivative, we will use the power rule of differentiation. The power rule states that if we have a function of the form f(x) = x^n, then the derivative is given by f'(x) = nx^(n-1).

In this case, the derivative of C(ρ) with respect to ρ is:

C'(ρ) = -1/9100p