Chapter 4.3, Problem 2TU

TEST YOUR UNDERSTANDING | FOR EXAMPLE $4.8$

A snake is growing towards its maximum length of $46\text{inches}$. The below table shows the difference $D$ between its maximum length of $46\text{inches}$ and its current length $L$. Both $D$ and $L$ are measured in $\text{inches}$.

$t=timeinyears$	$0$	$1$	$2$	$3$	$4$
$D=differenceinlength$	$25.00$	$18.75$	$14.06$	$10.55$	$7.91$

Find a model of the difference $D$ as an exponential function of the time $t$ in years. Find a function that gives the length $L$ in terms of $t$.