The following problem is a sinusoidal transformation Graph w

The following problem is a sinusoidal transformation. Graph (with labels) the function using t as the independent variable (x) and v as the dependent variable (v). Then clearly answer the questions. The volume of air, v, in cubic centimeters, in the lungs of a certain distance runner is modeled by the equation u = 400sm(60mt) + 900 where t is time in minutes. a) What are the maximum and minimum volumes of air in the runner\'s lungs at any time? b) How many breaths does the runner take per minute? Hints: . Follow the same process as the trig transformations we\'ve done to date: Asin[B(X-C)l+D. Graph the range, find the period and find the critical points. . Think about breaths per minute as frequency

Solution

a)
Max : 400 + 900 = 1300
Min : 400 - 900 = -500

b)
How many breaths per min?
Compare with Asin[B(t - C)] + D
400sin[60pi*t] + 900

Comparing
A = 400
B = 60pi
C = 0
D = 900

So, period = 2pi/B
period = 2pi/(60pi)
period = 1/30

So, in 1 minute, the runner takes 1 / (1/30 min)

30 breaths