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A population of 480 bacteria is introduced into a culture and grows in number according to the equation , where t is measured in hours. Find the rate at which the population is growing when t = 4. Round your answer to two decimal places. ​

Find the slope of the graph of the function at the given value. ​  when x = 7 ​

Use the Quotient Rule to differentiate the function .                   REMINDER:  

The design of a concept vehicle is intended to allow it to obtain energy from a rotating flywheel (solid disk), which has a radius of 2.00 m and a mass of 500 kg. Initially, the flywheel attaches to an electric motor in order to bring the flywheel’s rotational speed up to 7500 rev/min. What is the amount of stored kinetic energy in the flywheel in joules? How much time in hours could the vehicle continue to run before the flywheel would need to be brought back up to speed if the flywheel was used to supply energy to the car in the same way as a 25.0 hp motor? (Remember: 1 hp = 746 W and \(I = \frac{1}{2}mr^{2}\) for a solid disk)

Application Questions Solve the following computational problems and show your work. (6 points each)

A ping-pong ball collides with a bowling ball and sticks to the bowling ball. The initial momentum of the ping-pong ball is p, and the bowling ball is initially at rest. What is the momentum of the combined objects after the collision?

If a net torque is applied to a rigid object, that object will experience which of the following?

Suppose a billiard ball and a bowling ball are rolling down a smooth hill. If they both started at rest at the top of the hill, which one will reach the bottom first?

Conceptual Questions Select the correct answer for each of the following concept questions. (2 points each)

The impulse experienced by a body is defined as being equal to the change in which of the following quantities?