Course:MATH102/Question Challenge/2010 December 05
Question
When a person breathes, the volume of air in the lungs may be modelled by a function of the form
where V is the volume in millilitres and t is time in seconds. Suppose the minimum and maximum volumes are 1400 and 3400 ml respectively, and the maximum rate of change of V is 1200 ml/sec.
What is the period of V(t)?
Hints
Solutions
Solution |
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We are told that the minimum and maximum volumes are 1400 and 3400 ml. From this we find the mean to be (1400+3400)/2= 4800/2= 2400. We also find the amplitude to be (3400-1400)/2=2000/2=1000. Hence
The rate of change is , and we calculate this to be
The max rate of change will occur when the cosine term is -1, at which time . We also know that this rate is so 1200 ml/sec, so ml/sec. Hence /sec The period is given by: sec. |