Chapter 6.3, Problem 69E

a.

To determine

To determine the graph of the function using graphing calculator

Explanation of Solution

Given information:

Consider the given information provided,

The domain of function is $200\le A\le 35,000$

Graph:

The sketched is given for the function

  $s=30.6-20.5\log A+3.8{\left(\log A\right)}^2$

Interpretation:

From the graph, it is observed that a study in Florida found that the number S of fish species in a pool or lake can be observed by the pool or lake.

b.

To determine

To estimate the number of species in a lake with an area of 30,000 square meters

Answer to Problem 69E

The number of S fish species in a lake or pool is 14.99

Explanation of Solution

Given information:

Consider the given information provided,

The area of the lake or pool is 30,000 square meters.

Graph:

The sketched graph is given for $s=30.6-20.5\log A+3.8{\left(\log A\right)}^2$

Interpretation:

It is observed from the graph the number of S fish species is 14.99 in a lake with an area of 30,000 square meters.

c.

To determine

To estimate the area of a lake that contains six species of fish

Answer to Problem 69E

the area of a lake that contains six species of fish is 3917.2 square meters.

Explanation of Solution

Given information:

Consider the information given,

  $s=30.6-20.5\log A+3.8{\left(\log A\right)}^2$

The domain of the function,

  $200\le A\le 35,000$

Graph:

The sketched graph is given for $s=30.6-20.5\log A+3.8{\left(\log A\right)}^2$

Interpretation:

It is observed from the graph that the area of a lake that contains six species of fish is 3917.2 square meters.

d.

To determine

To determine what happens to the number of fish species as the area of a pool or lake increase

Answer to Problem 69E

The number of fish species increases as the area of a pool or lake increases.

Explanation of Solution

Given information:

Consider the information given,

  $s=30.6-20.5\log A+3.8{\left(\log A\right)}^2$

As the area of the pool or lake increases, more no. of fish species can be sustained in the lake or pool.