Problem. A man made lake initially contains 200 gal of water with 50 lb of a chemical dissolved into it. A solution containing 3 lb/gal of the chemical runs into the lake at a rate of 4 gal/min and the well mixed solution runs out of the lake at a rate of 4 gal/min. What is the maximum amount of chemical ever in the lake? A. Set up a differential equation modeling the amount of chemical in the lake at any time. (Choose your own notation, and clearly indicate meaning) B. Solve the differential equation. C. Based on the solution, answer the following: What is the maximum amount of chemical ever in the lake?

The rate of decay of a radioactive substance depends upon the amount present initially. the mass y (mg) of the radioactive substance cobalt-60 present in a sample at time t (years) is represented by the exponential equation y=50e −0.1315 t . answer the following questions in complete sentences. 1. how does the exponential equation above compare to the equation for simple interest that is compounded continuously? explain the similarities. 2. what is the initial amount of cobalt-60 in the sample? 2. how much cobalt-60 is left after 8.4 years? show your work. 3. what would be the y-intercept of the graph? what does it represent? 4. after how many years will the amount of cobalt-60 left be 6.25 mg? explain what happens to the cobalt-60 after 50 years? 5. discuss some “real-world” examples and uses of cobalt-60

Calculate the missing value. round the answer to on decimal place. start with 70, increase it by 21%, and end up with

Find an bif a = {3, 6, 9, 12) and b = {2, 4, 6, 8, 10).