Chapter 4.4, Problem 20E

Special Rounding Instructions. For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated.

Caloric Content Versus Shell Length In 1965, Robert T.Paine gathered data on the length $L$, in millimeters, of the shell and the caloric content $C$, in calories, for a certain mollusk. The table below is adapted from those data.

$L=length$	$C=Calories$
$7.5$	$92$
$13$	$210$
$20$	$625$
$24$	$1035$
$31$	$1480$

a. Find an exponential model of calories as a function of length.

b. Plot the graph of the data and the exponential model. Which of the data points show a good deal less caloric content than the model would predict for the given length?

c. If length is increased by $1\text{millimeter}$, how is caloric content affected?