Chapter 8.1, Problem 34PPS

a.

To determine

To calculate: function notation equation that gives the depth of the submersible as a function of the total time.

Answer to Problem 34PPS

The function notation equation that gives the total depth of submersible as a function of the total time is $d(t)=40t$

Explanation of Solution

Given information : submersible descends to a depth of $1500feet$ at a rate of $40feet/minute$

Let ‘d’ be the total depth and ‘t’ be the total time taken to explore an underwater shipwreck.

Since the total depth is directly proportional to the total time taken, which means as the depth increases time also increases of the shipwreck.

Therefore dependent and independent variables is identified and is as follows,

total depth is said to be a dependent variable while the total time is independent variable.

Function: $totaldepth=feetperminute\times totaltime$

  $d(t)=40t$

b.

To determine

The total time taken to reach $1500feet$ in $minutes$ .

Answer to Problem 34PPS

The total time taken to reach $1500feet$ is $37.5minutes$

Explanation of Solution

Given:

  $totaldepth=$ $d(t)$

  $totaltime$ $=$ $t$

Calculation:

Put the value of ‘d’ in the equation and solve it for ‘t’

  $\begin{array}{l}d(t)=40t\\ t=d÷40\\ t=1500÷40\\ t=37.5minutes\end{array}$

Conclusion:

The total time taken to reach

  $1500feet$ is $37.5minutes$