Chapter 1, Problem 10PS

Biorhythms A popular theory that attempts to explain the ups and downs of everyday life states that each person has three cycles, called biorhythms, which begin at birth. These three cycles can be modeled by the sine functions below, where $t$ is the number of days since birth.

Physical (23 days): $P=\sin \frac{2\pi t}{23},t\ge 0$

Emotional (28 days): $E=\sin \frac{2\pi t}{28},t\ge 0$

Intellectual (33 days): $I=\sin \frac{2\pi t}{33},t\ge 0$

Consider a person who was born on July $20,1995.$

(a) Use a graphing utility to graph the three models in the same viewing window for $7300\le t\le 7380.$

(b) Describe the person’s biorhythms during the month of September $2015.$

(c) Calculate the person’s three energy levels on September $22,2015.$