Question

Assume that the volume of air in an average adult’s lung follows a transformed sine

function, as function of time t in seconds,
V (t) = A + B sin(ωt)
Below is a table of measurements of the volume. Identify constants A, B, and ω so
that the function above fits these measurements. After 12 seconds, the measurements
will repeat.
t 0 3 6 9 12
V (t) 7 9 7 5 7

Answer 1

A = 7

B = 2

ω = π/6

Full Equation: V(t) = 7 + 2sin((π/6)t)

Explanation:

For this question, you simply have to acquire all the information necessary in order to construct a sine equation. You can easily do this by looking at your table of values (I would recommend graphing it for a visual aid).

From there you can observe that the graph is shifted up by 7 units (here is where we get the A value of 7).

The amplitude of the graph is 2 units (we can see this by comparing the highest point of the graph to its horizontal center line).

Finally, the period of the graph is obtained by setting 2π/ω equal to 12 (12 being the time it takes for the graph to do a full period). Here we get a value of π/6.