The remaining amount, A (in grams), of a substance undergoing ra- dioactive decay is given by the function A = f(t,C), where C is the initial amount of the substance present (in grams) and t is the time that has passed, in years. Use the contour plot of f shown to the right to answer the following questions. 40 15 20 30 20 (a) How much of the substance must be present in the initial sample in order for there to be 15 grams remaining after 2 years? Include 10 units. 1 2 3 4 (b) Sketch a graph of the cross-section of f in which t = 2. Carefully label your axes, and then briefly explain what this graph tells you. (c) Sketch a graph of the cross-section of ƒ in which C = 40. Carefully label your axes, and then briefly explain what this graph tells you.

- GROWTH OF TABLET AND SMARTPHONE USERS The number of tablets and smartphones in use worldwide (in millions) in year t from 2010 through 2012 can be approximated by f(t) = 128.111.94 (1Si 3) %3D where t = 1 corresponds to 2010. a. How many tablets and smartphones were in use in 2011? b. How fast was the number of tablets and smartphones changing in 2011?

Radium (Ra-225) has a half-life of 15 days. For a 100 g sample, the amount of radioactive material remaining, A, after time t, is given by the equation A(t) = 100(0.5) is, where A is measured in grams and t is measured in days. a. Find the average rate of change from 3 days to 4 days, rounded to one decimal place. b. Approximate the average rate of change at t = 3 days, rounded to one decimal place.