Everybodys blood pressure vanes over the course of the day I

Everybody\'s blood pressure vanes over the course of the day. In a certain individual the resting diastolic blood pressure at time f is given by B(t) = 70 + 5 sin(nt/12), is measured in hours since midnight and B(t) in mmH_ g (millimeters of mercury). Find this person\'s diastolic blood pressure at the following times. (Round your answers decimal place.) 3:00 A.M. mmHg 10:30 A.M. mmHg Noon mmHg 9;00 P.M. mmHg

Solution

blood pressure at time t is given by the function

B(t) = 70 + 5 sin ( pi*t / 12 )

blood pressure at 3 AM

time elapsed at 3AM since midnight = 3 hours

plugging t = 3

70 + 5 sin ( pi*(3) / 12 ) = 70 + 5 sin pi/4

= 70.5355

b ) 10:30 AM

time elapsed since midnight is 10.5 hours

plugging t = 10.5

70 + 5 sin ( pi*(10.5) / 12 ) = 71.9134

c) noon that is 12pm

time elapsed - 12 hours

70 + 5 sin ( pi*12 / 12 ) = 70

d) 9 pm

time = 21 hours

70 + 5 sin ( pi*21 / 12 ) = 66.464