Chapter 4.4, Problem 19E

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.

Growth in Length of Haddock A study by Raitt showed that the maximum length that a haddock could be expected to grow is about $53\text{centimeters}$.Let $D=D\left(t\right)$ denote the difference between $53\text{centimeters}$ and the length at age $t$ years. The table below gives experimentally collected values for $D$.

Age $t$	Difference $D$
$2$	$28.2$
$5$	$16.1$
$7$	$9.5$
$13$	$3.3$
$19$	$1.0$

a. Find an exponential model of $D$ as a function of $t$.

b. Let $L=L\left(t\right)$ denote the length in centimeters of a haddock at age $t$ years. Find the model for $L$ as a function of $t$.

c. Plot the graph of the experimentally gathered data for the length $L$ at ages $2,5,7,13$, and $19\text{years}$ along with the graph of the model you made for $L$. Does this graph show that the $5-\text{year}$ old haddock is a bit shorter or a bit longer than would be expected?

d. A fisherman has caught a haddock that measures $41\text{centimeters}$. What is the approximate age of the haddock?