Chapter 6.4, Problem 95AE

Biorhythms In the theory of biorhythms, a sine function of the form

$P\left(t\right)=50\sin \left(\omega t\right)+50$

is used to measure the percent $P$ of a person’s potential at time $t$, where $t$ is measured in days and $t=0$ is the day the person is born. Three characteristics are commonly measured:

Physical potential: period of 23 days

Emotional potential: period of 28 days

Intellectual potential: period of 33 days

(a) Find $\omega$ for each characteristic.

(b) Using a graphing utility, graph all three functions on the same screen.

(c) Is there a time $t$ when all three characteristics have $100\%$ potential? When is it?

(d) Suppose that you are 20 years old today ( $t=7305$ days). Describe your physical, emotional, and intellectual potential for the next 30 days.