Question

Each time your heart beats, your blood pressure first increases and then decreases as the heart rests between beats. The maximum and minimum blood pressures are calledthe systolic and diastolic pressures, respectively. Your blood pressure reading is written as systolic/diastolic. A reading of 120/80 is considered normal. A certainperson's blood pressure is modeled by the function p(t)=115 25sin (160pit) where p(t) is the pressure in mmHg, at time t measured in minutes. a) Find the period of pb) FInd the number of heartbeats per minute. c) Graph the function p d) find the blood pressure reading. How does this compare to normal blood pressure? The textbookanswer is period 1/80 min, and 80 heartbeats per minute, and blood pressure of 140/90. I couldn't find the graph on my calculator (what would be the right window?) andI don't understand why the period is 1/80 min and therefore 80 heartbeats per minute. Please help. Thank you.

Answer 1

a) period = is always 2 (pi) divided by the coefficient of t. So in your case:
period=2pi/160pi=1/80=0.0125 minutes

b) 0.0125 minutes/heartbeat = 80 heartbeats/minute (reciprocal)

c) Since the graph goes between 90 and 140 (as from part d) you want to make your y-min something like 80 and your y-max something like 150. If you leaveit at -10 to 10, you won't see anything. For x, I would make x-min 0 and x max 0.25. That way you'll see 15 seconds (1/4 of a minute) of heartbeats.

d) The midline of the graph is 115 (I'm assuming the equation is 115 + 25 sin (160 pi t), the plus sign is not showing up for me in your question. Theamplitude is 25. So 115+25=140 and 115-25 is 90. So high blood pressure because it's 140/90.

Hope this helps!

Answer 2

en.wikipedia.org/wiki/Hypertension