Chapter 8.1, Problem 24E

a.

To determine

As a skydiver falls, does the atmospheric pressure increase or decrease? Does the reading on skydiver’s altimeter increase or decrease?

Answer to Problem 24E

The atmospheric pressure will increase as a skydiver will fall.

The reading on skydiver’s altimeter will decrease.

Explanation of Solution

Given:

A skydiver uses an altimeter to track altitude so that he or she knows when to open the parachute. The altimeter determines altitude by measuring changes in atmospheric pressure. The graph below shows how pressure varies with altitude as a skydiver falls from 12,000 feet to ground level. (The elevation of the ground is assumed to be 0 feet with respect to sea level.)

  

Calculation:

Upon looking at our given graph, we can see that x -axis represents altitude of a skydiver in thousands of feet and y -axis represents atmospheric pressure in pounds per square feet.

Since the ground level will be at $x=0$ , so we can see as we move from right to left on our graph the altitude is decreasing and atmospheric pressure is increasing.

Therefore, the atmospheric pressure will increase as a skydiver will fall.

Since the altimeter determines altitude, so reading on skydiver’s altimeter will decrease.

b.

To determine

To describe:

The domain and range of the relation represented by the graph.

Answer to Problem 24E

The domain of the relation represented by the graph is $\left[0,12000\right]$ .

The range of the relation represented by the graph is $\left[1350,2150\right]$ .

Explanation of Solution

Given:

A skydiver uses an altimeter to track altitude so that he or she knows when to open the parachute. The altimeter determines altitude by measuring changes in atmospheric pressure. The graph below shows how pressure varies with altitude as a skydiver falls from 12,000 feet to ground level. (The elevation of the ground is assumed to be 0 feet with respect to sea level.)

  

Calculation:

Upon looking at our given graph, we can see that x values on our graph goes from $x=0$ to $x=12,000$ . Therefore, the domain of the relation is $\left[0,12000\right]$ .

We can also see that y values on our graph goes from $y=1350$ to $y=2150$ . Therefore, the range of the relation is $\left[1350,2150\right]$ .

c.

To determine

Is the relation a function? Explain.

Answer to Problem 24E

The given relation is a function as the graph passes vertical line test.

Explanation of Solution

Given:

A skydiver uses an altimeter to track altitude so that he or she knows when to open the parachute. The altimeter determines altitude by measuring changes in atmospheric pressure. The graph below shows how pressure varies with altitude as a skydiver falls from 12,000 feet to ground level. (The elevation of the ground is assumed to be 0 feet with respect to sea level.)

  

Calculation:

Upon looking at our given graph, we can see that any verticalwill not intersect our graph more than one place. Therefore, the given relation is a function.

d.

To determine

Some altimeters can sound an alarm warning a skydiver to open the parachute when the altitude falls to a certain level. If the alarm is set to go off at an altitude of 3000 feet, approximately what atmospheric pressure will trigger the alarm?

Answer to Problem 24E

An atmospheric pressure of 1900 pounds per square feet will trigger the alarm.

Explanation of Solution

Given:

A skydiver uses an altimeter to track altitude so that he or she knows when to open the parachute. The altimeter determines altitude by measuring changes in atmospheric pressure. The graph below shows how pressure varies with altitude as a skydiver falls from 12,000 feet to ground level. (The elevation of the ground is assumed to be 0 feet with respect to sea level.)

  

Calculation:

To solve our given problem, we need to check the value of y , when $x=3$ .

Upon looking at our given graph, we can see that the value of y is 1900 at $x=3$ . Therefore, anatmospheric pressure of 1900 pounds per square feet will trigger the alarm.