Medical research has shown that between heartbeats, the pressure in the aorta of a normal adult is a function of time in seconds and can be modeled by the equation P = 95e−0.491t. (a) Use the derivative to find the rate at which the pressure is changing at any time t. P'(t) =     (b) Use the derivative to find the rate at which the pressure is changing after 0.6 second. (Round your answer to one decimal place.)   ----   (c) Is the pressure increasing or decreasing? The pressure is increasing. The pressure is decreasing.

The shadow cast by a man standing 1 m from a lamppost is 1.2 m long. If the man is 1.8 m tall and walks away from the lamppost at a speed of 120 m/min, at what rate is the shadow lengthening after 5 s? Write what is given and what you need to find. Draw the diagram. Show the derivative step. Write the conclusion statement.

B.

• Find a formula for the nth derivative of y = 47ª, telling me how you decide what to do at each step.