In a normal respiratory cycle the volume of air that moves into and out of the lungs is about 498 mL. The reserve and residual volumes of air that remain in the lungs occupy about 1990 mL and a single respiratory cycle for an average human takes about 4 seconds. Find a model for the total volume of air V(t) in the lungs as a function of time.

The model is .

Step-by-step explanation:

Consider the given information.

The volume of air inside the lungs increases or decreases so for this we will use the basic sine function as our parent function.

Let us assume that the phase shift is 0 it means .

The air that moves into and out of the lungs is about 498 mL.

It means the amplitude of the function will vary by 249(half of 498).

The reserve and residual volumes of air that remains in the lungs occupy about 1990 mL which is the minimum air in the lungs.

So, the max air will be: 1990+498 =2488 mL

And the average will be d=1990+249=2239 ml

The horizontal stretch will be   as we know that period of is and respiratory cycle for an average human takes about 4 seconds.

Hence, the model is .

  y= -3x is the required function.

step-by-step explanation:

we have been given a table:

x             y

0             0

1             -3

3             -9

-2             6

we can see that the values of y is -3 times the value of x

hence, the function would be: y= -3x.

put the values of x will give the same y as in the table that means function is satisfying the given table.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."