Chapter 8.2, Problem 39E

a.

To determine

To approximate:

The fork length of each given species of shark to the nearest centimeter if the shark’s total length is 250 centimeters.

Answer to Problem 39E

Fork length of Bigeye thresher is 158 centimeters.

Fork length of scalloped hammerhead is 194 centimeters.

Fork length of white shark is 230 centimeters.

Explanation of Solution

Given:

The fork length of a shark is the distance from the tip of the shark’s snout to the fork of its tail, as shown:

  

The table lists equations giving the fork length f as a function of the total length t for three species of sharks, where both f and t are measured in centimeters.

  

Calculation:

To find the fork length of each species of shark, we will substitute $t=250$ in each equation as:

  $\begin{array}{l}f=0.560t+17.7\\ f=0.560(250)+17.7\\ f=140+17.7\\ f=157.7\\ f\approx 158\end{array}$

Therefore, the fork length of Bigeye thresher is 158 centimeters.

  $\begin{array}{l}f=0.776t-0.313\\ f=0.776(250)-0.313\\ f=194-0.313\\ f=193.687\\ f\approx 194\end{array}$

Therefore, the fork length of scalloped hammerhead is 194 centimeters.

  $\begin{array}{l}f=0.944t-5.74\\ f=0.944(250)-5.74\\ f=236-5.74\\ f=230.26\\ f\approx 230\end{array}$

Therefore, the fork length of white shark is 230 centimeters.

b.

To determine

To find:

For each species of shark, what percent of the total length does the fork length represent if the shark is 250 centimeters long? Round your answers to nearest percent.

Answer to Problem 39E

Fork length of Bigeye thresher is 63% of total length.

Fork length of scalloped hammerhead is 78% of total length.

Fork length of white shark is 92% of total length.

Explanation of Solution

Given:

The fork length of a shark is the distance from the tip of the shark’s snout to the fork of its tail, as shown:

  

The table lists equations giving the fork length f as a function of the total length t for three species of sharks, where both f and t are measured in centimeters.

  

Calculation:

We will find the fork length of each species is what percent of total length as:

  $\begin{array}{l}\text{Bigeye thresher}=\frac{158}{250}\cdot 100\%\\ \text{Bigeye thresher}=0.632\cdot 100\%\\ \text{Bigeye thresher}=63.2\%\\ \text{Bigeye thresher}\approx 63\%\end{array}$

Therefore, the fork length of Bigeye thresher is 63% of total length.

  $\begin{array}{l}\text{Scalloped hammerhead}=\frac{194}{250}\cdot 100\%\\ \text{Scalloped hammerhead}=0.776\cdot 100\%\\ \text{Scalloped hammerhead}=77.6\%\\ \text{Scalloped hammerhead}\approx 78\%\end{array}$

Therefore, the fork length of scalloped hammerhead is 78% of total length.

  $\begin{array}{l}\text{White shark}=\frac{238}{250}\cdot 100\%\\ \text{White shark}=0.92\cdot 100\%\\ \text{White shark}=92\%\end{array}$

Therefore, the fork length of white shark is 92% of total length.

c.

To determine

Which species of shark do you think has the longest tail relative to its body size? Explain your reasoning.

Answer to Problem 39E

The white shark has the longest tail.

Explanation of Solution

Given:

The fork length of a shark is the distance from the tip of the shark’s snout to the fork of its tail, as shown:

  

The table lists equations giving the fork length f as a function of the total length t for three species of sharks, where both f and t are measured in centimeters.

  

Calculation:

We can see from the calculations of part (a) and part (b) that white shark has the longest fork length and its fork length is 92% of the total length.

Therefore, the white shark has the longest tail.