If the annual rate of inflation averages over the next  years, the approximate cost  of goods or cervices during any year in that decade is where  is the time in years and  is the present cost. The price of an oil change for your car is presently. Estimate the price years from now. Round your answer to two decimal places. ​

Find the derivative of the function .  ​

A conical tank (with vertex down) is 12  feet across the top and 18  feet deep. If water is flowing into the tank at a rate of 18  cubic feet per minute, find the rate of change of the depth of the water when the water is 10  feet deep. ​

In a free-fall experiment, an object is dropped from a height of 256 feet. A camera on the ground 500 feet from the point of impact records the fall of the object as shown in the figure. Assuming the object is released at time . At what time will the object reach the ground level? ​ ​

A point is moving along the graph of the function  such that  centimeters per second. Find  when . ​

A petrol car is parked 50 feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of 30 revolutions per minute. How fast is the light beam moving along the wall when the beam makes an angle of  with the perpendicular from the light to the wall.  ​

Use the Product Rule to differentiate. ​ ​

A buoy oscillates in simple harmonic motion as waves move past it. The buoy moves a total of feet (vertically) between its low point and its high point. It returns to its high point every seconds. Determine the velocity of the buoy as a function of t. ​

Suppose a 20-centimeter pendulum moves according to the equation where is the angular displacement from the vertical in radians and t is the time in seconds. Determine the rate of change of when seconds. Round your answer to four decimal places. ​

A buoy oscillates in simple harmonic motion as waves move past it. The buoy moves a total of 10.5 feet (vertically) between its low point and its high point. It returns to its high point every 16 seconds. Write an equation describing the motion of the buoy if it is at its high point at t = 0. ​