Question

The monthly sales of Sunny Electronics' new sound system are given by q(t)=4000t−100t² units per month, t months after its introduction. The price Sunny charges is p(t)=2000−t² dollars per sound system, t months after introduction. Find the rate of change of monthly sales.

Answer 1

Answer:

The rate of change with respect to monthly sales is 4000 - 200t.

Step-by-step explanation:

The sales per month (monthly sales) of the new sound system being sold by Sunny Electronics is given by q(t)  = 4000t - 100$t^2$ units per month, where t is number of months from the introduction of the sound system.

The price of each unit of the sound system charged by Sunny Electronics is given by p(t) = 2000 - $t^2$.

The rate of change with respect to monthly sales will be given by the equation

$\frac{dq(t)}{dt} = \frac{d(4000t - 100t^2)}{dt} = 4000 - 200t$.