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related rates

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jeff mapes

on 7 December 2012

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Transcript of related rates

What do we know? Lets solve this Blood circulation problem 4.6
Related rates What are we looking for? we will be finding dc/dt or the rate of change of the circulation time using the given information. P=17.4
mass of child is=x=45kg
rate of growth=dx/dt=.1kg/month
y=px^(1/4) P=x^(1/4)
dp/dt=(1/4)x^(-3/4)dx/dt
Plug in what we know The circulation time of a mammal (that is, the average time it takes for all blood in the body to circulate once and return to the heart) is proportional to the fourth root of the body mass of the mammal. The constant of proportionality is 17.40 if circulation time is in seconds and body mass is in kilograms. The body mass of a growing child is 45kg and is increasing at a rate of 0.1kg/month. What is the rate of change of the circulation time of the child? The problem Jeffery Mapes
Lucas Herschbach Y=17.4*(x^1/4)
dY/dt=4.35(x^-3/4)dx/dt
dy/dt=(4.35/45kg^(3/4))0.1kg/month
dY/dt=0.025sec/month The rate of which the childs circulation is increasing is 0.025 sec/month Our Math Conclusions
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