Chapter 5.4, Problem 17E

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

Gray Wolves in Michigan Gray wolves recolonized in the Upper Peninsula of Michigan beginning in $1990$. Their population has been documented as shown in the following table. ${}^{56}$

a. Explain why one expect an exponential model to be appropriate for these data.

b. Find an exponential model for the data given.

Year	Wolves
$1990$	$6$
$1991$	$17$
$1992$	$21$
$1993$	$30$
$1994$	$57$
$1995$	$80$
$1996$	$116$
$1997$	$112$
$1998$	$140$
$1999$	$174$
$2000$	$216$

c. Graph the data and the exponential model. Would it be better to use a piecewise-defined function?

d. Find an exponential model for $1990$ through $1996$ and another for $1997$ through $2000$.

e. Write a formula for the number of wolves as a piecewise-defined function using the two exponential models. Is the combined model a better fit?