**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 N is a constant and _{o}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 (ii) What is the value of (iii) What is the change in (iv) What is the average rate of change in (v) Can you use the result of (iv) to obtain the rate of change of |

**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*