Chapter 4.5, Problem 6STP

A plane was flying at an altitude of 30,000 feet when it began the descent toward the airport. The airplane descends at a rate of 850 feet per minute.

a. What is the function rule that describes this situation?

b. What is the altitude of the plane after it has descended for 8 minutes? Show your work.

c. Use the function in part a to determine how long it takes for the plane to land if it descends at a continuous rate.

To determine

The function rule that describe the given situation.

Answer to Problem 6STP

Function rule is given below;

  $\text{S}=30,000-850\times \text{t}$ .

Explanation of Solution

Given:

Plane was flying at an altitude of $30,000$ feet when it began the desent towards the airpot .

The airplane descends at a rate of $850$ feet per minute .

Let $\text{S}$ be the altitude. ( $\text{S}$ is measured in feet)

So, define the function according to the situation.

  $\text{S}=30,000-850\times \text{t}$ ;

Where,

t: time in minute.

To determine

The altitude of the plane after it has descended for $8$ minutes.

Answer to Problem 6STP

The altitude of the plane after it has descended for $8$ minutes is $\text{S}=23,200$ feet.

Explanation of Solution

Given:

Plane was flying at an altitude of $30,000$ feet when it began the desent towards the airpot .

The airplane descends at a rate of $850$ feet per minute .

After 8 minutes plane`s altitude:

  $\begin{array}{l}\text{S}=\text{}30,000-850\times 8\\ \text{S}=\text{}30,000-6800\\ \text{S}\text{=}3200\text{feet}\end{array}$

To determine

Time taken for the plane to land if it descends at a continuous rate.

Answer to Problem 6STP

It takes $\text{t = 35}\text{.294}$ minutes for the plane to land if it descended at a continuous rate.

Explanation of Solution

Given:

Plane was flying at an altitude of $\text{30,000}$ feet when it began the desent towards the airpot .

The airplane descends at a rate of $\text{850}$ feet per minute .

For plane to land, altitude $\text{S}=0$

That is:

  $\begin{array}{l}30,000-850\times \text{t}=0\\ 850\text{t}=30,000\\ \text{t}=35.294\text{minutes}\end{array}$