University of Maryland
Department of Physics

Math Diagnostic

 1 The number of bacteria A in a culture at time t after observations begin is f(t) where , where No is a constant and t is in hours. The number of bacteria B in the same culture at time t is g(t) where . (Note e~2.7) Which bacteria is growing at a faster rate one hour after observations begin? Explain how you arrived at your answer. Which bacteria population is greater after 1 hour? Explain how you arrived at your answer.
 2 Explain in words, using the graph, why , where a is a constant between 0 and 3.
 3 Find the largest possible area of a rectangle with its lower base on the x-axis and upper vertices on the curve
 4 The graph represents the curve , from x=0 to x=4. (i) What is the value of y when x=a? (ii) What is the value of y when x=a+h? (iii) What is the change in y as x increases from a to a+h? (iv) What is the average rate of change in y in the interval where x increases from a to a+h? (v) Can you use the result of (iv) to obtain the rate of change of y at x=2.5? at x=b? If so how?

*These problems were adapted from problems developed by M.K. Heid, A Orton, and P. White and M. Mitchelmore.