Chapter 6.3, Problem 67E

a.

To determine

To graph: The given function.

Explanation of Solution

Given information:

  $l=27.1\ln w-32.8$

  $l$in inches and $w$ is in pounds.

Graph:

  

Interpretation:

The graph is of a logarithmic function. The curve is bounded in 1^st and 2^nd quadrant.

b.

To determine

To find: The weight of an alligator that is $10$ feet long using the graph.

Answer to Problem 67E

The weight of an $10$ feet long alligator is $281.006$ pounds.

Explanation of Solution

Given information:

  

Concept used:

From the graph we find corresponding value of $w$ when $l=10\text{ feet}=10\times 12\text{ inches }=120$

Calculation:

  

So, the weight of an alligator that is $10$ feet long is $281.006$ pounds.

c.

To determine

To identify: The x-intercept of the graph of the function. Explain whether the x-value make any sense in the context of the situation.

Answer to Problem 67E

x-intercept is at $\left(3.355,0\right)$ . This x-value makes no sense.

Explanation of Solution

Given information:

  

Concept used:

Shall use zero feature to find the x-intercept of the graph of the function.

Using zero feature we get the x-intercept at $\left(3.355,0\right)$

Se, we can say $l=0$ when $w=3.355$ .

No, this x-value makes no sense in the context of the situation because it is absurd to assume that a alligator has weight $3.355$ pound when it has no length (i.e. body less).