Question 170913: A person’s blood pressure, P(t), in millimeters of mercury (mm Hg), is modeled by the function P(t)=100=20cos(8π/3t), where t is the time in seconds.
a)What is the period of the function?
b)What does the value of the period mean in this situation?
c)Calculate the average rate of change in a person’s blood pressure on the interval [0.2,0.3]
d) Estimate the instantaneous rate of change in a person’s blood pressure at t=0.5.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A person’s blood pressure, P(t), in millimeters of mercury (mm Hg), is modeled by the function P(t)=100+20cos(8π/3t), where t is the time in seconds.
------------------
Form: y = acos(bx+c)+d
Period = b/(2pi)
-----------------------------
a)What is the period of the function?
Period = (8pi/3)/2pi = (4/3)pi
------------------------------
b)What does the value of the period mean in this situation?
The time between highest pressure and the next occurrence of highest
pressure is (4/3)pi seconds
------------------------------
c)Calculate the average rate of change in a person’s blood pressure on the interval [0.2,0.3]
--
P(t)=100+20cos(8π/3t)
Average = [P(0.3)-P(0.2)]/[0.3-0.2]
---------------------------------------
d) Estimate the instantaneous rate of change in a person’s blood pressure at t=0.5.
P(t)=100+20cos(8π/3t)
The instataneous rate of change at any time "t" is the derivative of P(t).
P'(t) = -20sin(8pi/3t)*(8pi/3)lnt
P'(0.5) = -20sin(16pi/3)*(8pi/3)ln(0.5)
etc.
==================
Cheers,
Stan H.
|
|
|
