Circadian rhythms are biological processes that oscillate with a period of approximately 24 hours. That is, a circadian rhythm is

Question

Circadian rhythms are biological processes that oscillate with a period of approximately 24 hours. That is, a circadian rhythm is an internal daily biological clock. Blood pressure appears to follow such a rhythm. For a certain individual the average resting blood pressure varies from a maximum of 100 mmHg at 2:00 P.M. to a minimum of 80 mmHg at 2:00 A.M.
Find a sine function of the form f(t) = a sin(ω(t − c)) + b
that models the blood pressure at time t, measured in hours from midnight.

phucdien · Answer

The equation becomes of the pressure is    P = 90 + 10 sin(π/36(t +4 ))     By observation the sine function should be of form P=  90 + 10 sin(ω(t − c)) as it  oscillates about 90 and with a factor of 10 . Let time be represented by the variable t in hours from 12.00 AM.   At 2:00 P.M. that is t= 14 hours the pressure is 100 mmHg  Substituting it in the equation we get,  100 = 90 + 10 sin(ω(t − c))  10 = 10  sin(ω(14 − c))  1 = sin(ω(14 − c))  ω(14 − c) = π/2                           -1)  At 2:00 A.M. that is t= 2 hours the pressure is 80 mmHg  80 = 90 + 10 sin(ω(t − c))  -10 = 10 sin(ω(2 − c))  3π/2 = ω(2 − c)                           -2)  dividing 2) with 1) we get  3 = (14 − c) /(2 − c)    6 - 3c = 14 - c  2c = -8   c = - 4   Substituting the value of c in 1) we get,  ω(14 − (-4)) = π/2   ω18 =  π/2    ω = π/36   Thus the equation becomes   P = 90 + 10 sin(π/36(t +4 ))       Learn more about  Sine  here :  https://brainly.com/question/17149483    #SPJ1

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