Chapter 8.1, Problem 34PPS

(a)

To determine

To identify: the independent and dependent variables.

Answer to Problem 34PPS

The required function is $d\left(t\right)=40t$

Explanation of Solution

Given:

The submersible descends to a depth of 1500 feet at a rate of 40 feet per minute

Calculation:

Let d be the total depth and t be the total time

Since the total depth depends on total time, total depth d be the dependent variable and total time t be the independent variable.

Words: $\text{Total depth}=\text{feet per minute }\times \text{ total time}$

Function: $d\left(t\right)=40t$

Conclusion: Therefore, the required function is $d\left(t\right)=40t$

(b)

To determine

To find: the total amount of time it took to reach 1500 feet.

Answer to Problem 34PPS

The total time to reach 1500 feet is 37.5 minutes.

Explanation of Solution

Calculation:

Need to find the total time to reach 1500 feet

Consider the equation

  $d\left(t\right)=40t$

Substitute $d\left(t\right)=1500$ in above equation

  $\begin{array}{l}1500=40t\\ \frac{1500}{40}=t\text{ Divide each side by 40}\\ \text{37}\text{.5=}t\end{array}$

Conclusion: Therefore, the total time to reach 1500 feet is 37.5 minutes.