Chapter 13.6, Problem 44E

(a)

To determine

To find: Thesequence representing the temperature decrease per $1000\text{feet}$ .

Answer to Problem 44E

The sequence of the temperature is $80,75,70,65,\mathrm{60.....}\text{and so on}\text{.}$

Explanation of Solution

Given: The temperature at ground level is $80$ F, and it decreases $5^0$ for each $1000$ feet.

Concept used:

A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

Calculation:

The temperature at ground level is $80$ F, and it decreases $5^0$ for each $1000$ feet, so the sequence representing the temperature is:

  $80,75,70,65,\mathrm{60.....}\text{and so on}\text{.}$

Hence, the sequence of the temperature is $80,75,70,65,\mathrm{60.....}\text{and so on}\text{.}$

(b)

To determine

To find: Theformula for the temperature $T$ in terms of height of the air $n$ .

Answer to Problem 44E

The formula for the temperature $T$ in term of $n$ is $T=80-5n$ .

Explanation of Solution

Given:

The temperature decreases $5^0$ for each $1000$ feet.

Concept used:

As the height of the air increase the temperature started to decrease at rate of

  $5^0$ per $1000\text{ feet}$ .

the formula will be:

  $T=80-5n$ .

Where at ground or $n=0$ the temperature will be ${80}^0$ .

Calculation:

The temperature decreases $5^0$ for each $1000$ feet, so, the formula is:

  $T=80-5n$ .

Where $n$ is the height of the air in the thousands of $\text{feet}$ .

Hence, the formula for the temperature $T$ in term of $n$ is $T=80-5n$ .

(c)

To determine

To find: The ground level temperature if the air is at $40000\text{ feet}$ and the temperature is $-{125}^{0}C$ .

Answer to Problem 44E

The ground level temperature is ${75}^0$ C.

Explanation of Solution

Given:

The temperature decreases $5^0$ for each $1000$ feet.

Concept used:

As the height of the air increase the temperature started to decrease at rate of

  $5^0$ per $1000\text{ feet}$ .

the formula will be:

  $T=T_g-5n$ .

Where at ground or $n=0$ .

  $n=\frac{\text{given air feet}}{1000}$ .

Calculation:

Let $T_g$ be the ground level from part $b$ and the formula after derived is

  $T=T_g-5n$ .

Where $n$ is the height of the air in the thousands of $\text{feet}$ .

First determine $n$ :

  $n=\frac{40000}{1000}=40$ .

According to the formula:

  $T=T_g-5n$ .

  $-125=T_g-5\left(40\right)$ .

  $-125=T_g-200$ .

  $-125+200=T_g$ .

  $T_g=75.$

Hence, the ground level temperature is ${75}^0$ C.