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.
| University of Maryland | Physics Department | PERG UMD | Project Links |
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Please address questions and comments about this diagnostic to
Mel Sabella.
email: msabella@delphi.umd.edu