Suppose that Magnus' blood pressure can be modeled by the following function
{{{p(t)=83-18sin(71pi*t)}}}
Magnus' blood pressure increases each time his heart beats, and it decreases as his heart rests in between beats. In this equation, p(t)is the blood pressure in mmHg (millimeters of mercury), and t is the time in minutes.
Find the following. If necessary round to the nearest hundredth.
Amplitude of p
Number of heartbeats per minute
Time for one full cycle of p
sin(anything) lies between -1 and +1
so -18sin(71π t) lies between -18 and +18
then p lies between 83-18 and 83+18
or between 65 and 101
period of your function = 2π/(71π) = 2/71 min
or appr 1.69 seconds
1.69 seconds = 1 beat
1 second = 1/1.69 beats
60 seconds = 60/1.69 beats= 35.5 beats
Use my analysis to answer your questions.
To find the amplitude of p, we need to determine the maximum and minimum values of p(t) and then find the difference between them.
The general form of a sinusoidal function is given by f(t) = Asin(Bt + C) + D, where A is the amplitude, B is the frequency, C is the phase shift, and D is the vertical shift.
From the given function p(t) = 83 - 18sin(71πt), we can see that the amplitude is the coefficient in front of the sine function, which is 18.
So, the amplitude of p is 18 mmHg.
Next, let's find the frequency, which represents the number of heartbeats per minute. In a sinusoidal function, the frequency is related to the coefficient of t.
In the given function p(t) = 83 - 18sin(71πt), the coefficient of t is 71π.
We know that the general formula for finding the frequency is f = B/(2π), where B is the coefficient of t.
Therefore, the frequency is f = 71π/(2π) = 71/2.
Therefore, the number of heartbeats per minute is 71/2.
To find the time for one full cycle of p, we need to determine the period of the function. The period is the time it takes for the function to complete one full cycle.
In the given function p(t) = 83 - 18sin(71πt), the coefficient inside the sine function is 71π.
The general formula for finding the period is T = (2π)/B, where B is the coefficient inside the sine function.
Therefore, the period is T = (2π)/(71π) = 2/71.
Therefore, the time for one full cycle of p is 2/71 minutes.