Chapter 1.2, Problem 21E

Reminder Round all answers to two decimal places unless otherwise indicated.

Yellowfin Tuna Data were collected comparing the weight $W$, in pounds, of a yellowfin tuna to its length $L$, in centimeters. These data are presented in the following table.

$L=Length$	$W=Weight$
$70$	$14.3$
$80$	$21.5$
$90$	$30.8$
$100$	$42.5$
$110$	$56.8$
$120$	$74.1$
$130$	$94.7$
$140$	$119$
$160$	$179$
$180$	$256$

a. What is the average rate of change, in weight per centimeter of length, in going from a length of $100$ centimeters to a length of $110$ centimeters?

b. What is the average rate of change, in weight per centimeter of length, in going from $160$ to $180$ centimeters?

c. Judging from the data in the table, does an extra centimeter of length make more difference in weight for a small tuna or for a large tuna?

d. Use the average rate of change to estimate the weight of a yellowtuna fish that is $167$ centimeters long?

e. What is the average rate of change, in length per pound of weight, in going from a weight of $179$ pounds to a weight of $256$ pounds?

f. What would you expect to be the length of a yellow tuna weighing $225$ pounds?