A worker at a snack stand opened a new box of cups. The first day, the worker used 30 cups from the box. The second day, the worker used 15% of the remaining cups in the box. A total of 90 cups were used on the second day. What was the original number of cups in the box before any cups were used?

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

Write an inequality and solve each problem.for exercises 11 and 12, interpret the solution.

Evaluate cos2θ for cosθ = square root of 3/2