If a rock is dropped from a height of 45 ft, its poistion t seconds after it is dropped until it hits the ground is given by the function s(t) = - 16t? + 45. Round values below to 3 decimal places. How long does it take the rock to hit the ground? seconds Find the average velocity of the rock from when it is released until when it hits the ground. feet per second What time after the rock is thrown will its instantaneous velocity be equal to its average velcity? (Apply the Mean Value Theorem) seconds after it is thrown

The half-life of plutonium-244 is 80,000,000 years. Find function gives the amount of carbon-14 remaining as a function of time, measured in years.

Change the function y=3(0.5)x to one having e as the base.

Find the unknown value. 27. y varies jointly with x and the cube root of 2. If when x=2 and z=27,y=12, find y if x=5 and z=8.

A Skydiver When a skydiver jumps from an airplane, his downward velocity, in feet per second, before he opens his parachute, is given by v=1761-0.834t, where t is the number of seconds that have elapsed since he jumped from the airplane. What is the velocity after 5 seconds?

What is the composition of two functions, fg ?

A rain drop hitting a lake makes a circular ripple. If the radius, in inches, grows as a function of time in minutes according to r(t)=25t+2 , find the area of the ripple as a function of time. Find the area of the ripple at t=2 .

The height of a projectile fired vertically into the air neglecting air resistance at an initial velocity of 64 feet per second is a function of the time (t) and is given by the equation h(t)=64t16t2 Compute h(1), h(2), h(3) and h(4).

A ball is dropped from the top of a lighthouse that is 145 feet above sea level. The height (position) of the ball after t seconds can be found using the function s(t) = -16t² + 145 Write all answers in decimal form, rounded to three decimal places where appropriate. A. Find the average rate of change of the ball on the interval from 1 to 1.5 seconds. Include the units. B. Find the instantaneous rate of change of the ball 2 seconds after it is dropped. Include the units. C. Find the height of the ball 2 seconds after it is dropped. Include the units. Type your answers into the box below. Be sure to label your answers A, B, and C.

Differentiate the function.snip4