Chapter 9.1, Problem 34HP

To determine

To express:The relationship between water depth and time to ascend to the water’s surface as a function. Explain the relationship between the variable. Also, explain whether water depth can ever correspond to two different times.

Answer to Problem 34HP

The given relation is a function.

Explanation of Solution

Formula used:

Distance is given by the formula:

  $\text{Distance = speed}\times \text{time}$

Let depth be d.

Let total time taken be t .

Let speed be s.

The relationship between water depth and time to ascend to the water’s surface as a function can be evaluated as follows:

Words $\text{Distance = speed}\times \text{time}$

Function $d(t)=st$

Here, the time taken t is the independent variable and distance or depth d is the dependent variable. Hence, the value of d is dependent on the value of t .

Water depth will never correspond to two different times if the speed, s is constant. If speed is changed, keeping the distance constant, then water depth can correspond to two different times.