Question

An athlete was having her blood pressure monitored during a workout. The doctor found that the periodic function, P= 20 sin (8pi/3 t) + 90 models her blood pressure as a function of time in seconds.

a. What is the systolic pressure (the maximum blood pressure)?

b. What is the diastolic pressure (the minimum blood pressure)?


c. What is the length in time, of her heartbeat cycle?


d. Sketch a wall labeled graph.

Answer 1

(a) 110 mm Hg

(b) 70 mm Hg

(c) 3/4 second

(d) see the attachment

Explanation:

(a) The sine function has a maximum value of +1, so the maximum value of p is ...

pmax = 20·(+1) +90 = 20+90 = 110 . . . . . mm Hg

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(b) The sine function has a minimum value of -1, so the minimum value of p is ...

pmin = 20·(-1) +90 = -20+90 = 70 . . . . . mm Hg

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(c) The period of the sine function is 2π, so the value of t that makes the argument be 2π will be the period.

8π/3·t = 2π

t = 2π·3/(8π) = 3/4 . . . . . . multiply by the inverse of the coefficient of t

The period of her heartbeat cycle is 3/4 seconds.

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(d) a graph is attached.