Biorhythms In the theory of biorhythms, a sine function of the form P ( t ) = 50 sin ( ω t ) + 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 ω 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.
Biorhythms In the theory of biorhythms, a sine function of the form P ( t ) = 50 sin ( ω t ) + 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 ω 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.
Solution Summary: The author explains how to find the amplitude and period of y, physical, emotional, and intellectual potentials.
Biorhythms In the theory of biorhythms, a sine function of the form
is used to measure the percent
of a person’s potential at time
, where
is measured in days and
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
for each characteristic.
(b) Using a graphing utility, graph all three functions on the same screen.
(c) Is there a time
when all three characteristics have
potential? When is it?
(d) Suppose that you are 20 years old today (
days). Describe your physical, emotional, and intellectual potential for the next 30 days.
7.
The number of visible sun spots varies rhythmically from 10
to 110 per year over a period of eleven years. The 110 max last
occurred in the year 2014.
a.)
b.)
Write a sinusoidal function N (t) to model that number of sun
spots per year, where t is in years past the year 2014.
What number of sun spots does your function predict for the
year 2018?
Chapter 6 Solutions
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