Chapter 8.7, Problem 28E

a.

To determine

To approximate:

The mass of the squid.

Answer to Problem 28E

The mass of the squid is approximately 667 grams.

Explanation of Solution

Given:

An arrow squid has a beak used for eating. Given the length b (in millimeters) of an arrow squid’s lower beak, you can approximate the squid’s mass (in grams) using function $m(b)=236b-513$ .

The beak of an arrow squid washes ashore on beach, where it is found and measured by a biologist. The lower beak has a length of 5 millimeters.

Calculation:

To solve our given problem, we will substitute $b=5$ in our given function as shown below:

  $\begin{array}{l}m(b)=236b-513\\ m(b)=236(5)-513\\ m(b)=1180-513\\ m(b)=667\end{array}$

Therefore, themass of the squid is approximately 667 grams.

b.

To determine

To approximate:

How long is the lower beak of an arrow squid to the nearest tenth of a millimeter with a mass of 1100 grams?

Answer to Problem 28E

The length of the lower beak of an arrow squid would be approximately 6.8 millimeters.

Explanation of Solution

Given:

An arrow squid has a beak used for eating. Given the length b (in millimeters) of an arrow squid’s lower beak, you can approximate the squid’s mass (in grams) using function $m(b)=236b-513$ .

The beak of an arrow squid washes ashore on beach, where it is found and measured by a biologist. The lower beak has a length of 5 millimeters.

Calculation:

To find the length of the lower beak of an arrow squid we will substitute $m(b)=1100$ in our given function as shown below:

  $\begin{array}{l}m(b)=236b-513\\ 1100=236b-513\\ 236b-513=1100\\ 236b-513+513=1100+513\\ 236b=1613\\ \frac{236b}{236}=\frac{1613}{236}\\ b=6.83474\\ b\approx 6.8\end{array}$

Therefore, thelength of the lower beak of an arrow squidwould be approximately 6.8 millimeters.