You place a tray of 60°F water in a freezer that is set at 0°F. The water cools according to Newton's Law of Cooling T (t) = T, + (To T,) e-kt where T is temperature, t is the number of hours the tray is in the freezer, T, is the temperature of the surrounding air, and To is the original temperature of the water. The water freezes in 4 hours. What is the S cooling constant, k? (hint: water freezes at 32°F Round your answer to the nearest hundredth.

A nkcschools.instructure.com Near the surface of any planet, the distance D fallen by a rock in time t is given by ct(this is a consequence of Newton's 2nd law of gravitation). Here we will D = measure D in feet and t in seconds. (a) A rock is dropped from two different heights. It takes the rock 5 times as long to hit the ground from the taller height. How do the heights compare? The taller height is times as tall as the other. (b) On Venus, a rock dropped from 70 feet above the surface takes 2.2 seconds to strike the ground. What is the value of c for Venus? Round your answer to 2 decimal places. (c) Another rock is dropped on Venus. How far has it fallen after 4 seconds? Round your answer to 2 decimal places and include an appropriate label.

A pizza is put in an oven with a constant temperature of 230 degree Celsius. The initial temperature of the pizza was 15 degree and one hour later, it became 65 degree. How long will it take for the pizza's temperature to become 80 degree? (Feel free to use the solution we obtained for Newton's law of cooling. Notice that in this problem we are heating an object. The only difference is the constant k being positive)

The intensity I of light (in lumens) at a distance x meters below the surface is given by I = I0 k x, where I0 is the intensity at the surface and k depends on the clarity of the water. At one location in the Atlantic Ocean, I0 = 14 and k = 0.7. Find the intensity of light at a depth of 11 meters. (Round your answer to three decimal places.)