University of Maryland
Department of Physics
|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
(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.
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