1. Show that "the rate of change of y is proportional to y" supports the model y = Cekx. 2. If BY = 4 , k is a constant, and if y = 3 when x = 1, and y = 8 when x = e, find y when x = 2. 3. The rate of change of y is proportional to y. When x = 0, y = 24, and when x = 2, y = 38. What is the value of y when x = 10?4. During a chemical reaction, substance A is converted to substance B at a rate that is proportional to the square of the amount of A. Let A(t) be the amount of unconverted substance A at any time t. Initially, there are 50 grams of substance A, after 2 hours there are only 10 grams remaining. How much of substance A is present after 4 hours? 5. Radioactive radium has a half-life of approximately 1599 years. A. If 50 milligrams of pure radium is present, initially, when will the amount remaining be 20 milligrams? Give your answer to the nearest year. B. What percent of a given amount remains after 100 years? 6. Water is leaking out of a large barrel at a rate proportional to the square root of the depth of the water at that time. If the water level starts at 36 inches and drops to 34 inches in 1 hour, how long will it take for all of the water to drain out of the barrel?7. Use the slope field at right to sketch the particular solution through the point (0, -=). Then, use integration to find the particular solution of the differential equation. dy = xe-0.2x2 dx 8. Verify that y = = - 1 is a solution of the differential equation: x y" + x y' - xy = x 9. The rate at which ice is melting in a small pond is given by = = v1 + 34 , where Vis the volume of ice in cubic feet and t is the time in minutes. What amount of ice has melted in 6 minutes? Round your answer to the nearest cubic foot. 10. Three months after a car dealership stopped advertising, the general manager observed that its monthly sales decreased from 312 vehicles per month to 208 vehicles per month. If the sales continue this same exponential pattern of decline, what will the sales be after another 2 months? Round your answer to the nearest whole number of vehicles