Chapter 4.4, Problem 60PS

Solution

To graph: The given function and use it to determine the alligator’s weight.

  $281$ pounds

Given:

The function $l=27.1\ln w-32.8$ and the alligator’s length $=10\text{ feet}$

Calculation:

To graph the function, find the value of $l$ at different values of $w$.

When $w=1$ the value of $l$ is,

  $\begin{array}{l}l=27.1\ln 1-32.8\\ l=-32.8\end{array}$

When $w=4$ the value of $l$ is,

  $\begin{array}{l}l=27.1\ln 4-32.8\\ l=4.769\end{array}$

Similarly, obtain more coordinate points for convenience. The following graph has been obtained using the computed coordinates.

  

It is understood that $1\text{ feet }=12\text{ inch}$ . So, $10\text{ feet }=120\text{ inch}$.

Here in the graph, the $y$ -axis is representing length and the $x$ -axis is representing weight. So,

When $y=120$ the value of $x$ or weight is $281$ that can be observed in the following graph.

  

Conclusion:

The weight of alligator is $281$ pounds.