The price (in dollars) of a computer component is P = 4C – 18C-1, where C is the manufacturer's cost to produce it. Assume that the cost at time t (in years) is C = 9 + 5t¬l and determine the rate of change of the price with respect to time at %3D t = 3. (Use decimal notation. Give your answer to three decimal places.) dP \dollars/year dt

A weight is suspended on a spring and set in motion such that it bobs up and down vertically. The equation h(t) = 3cos(3pi(t))+ 5 can be used to represent the height, h, in centimeters, of the weight above a desk after time, t, in seconds. Determine the instantaneous rate of change of the height at t = 3.5 seconds.

Give a real life example of where you might be interested in the rate of change of y relative to x. That is, replace “y” with a variable name, and “x” with a variable name (e.g., y = heart rate, x = running speed

The air in a room 15 ft by 12 ft by 12 ft is 3% carbon monoxide. Starting at t=0, fresh air containing no carbon monoxide is blown into the room at a rate of 300 ft/min. If air in the room flows out through a vent at the same rate, when will the air in the room be 0.01% carbon monoxide? The air in the room will be 0.01% carbon monoxide after (Round to two decimal places as needed.) minutes.