Chapter 5.1, Problem 14E

Long-Term Data and the Carrying Capacity This is a continuation of Exercise 13. Ideally, logistic data grow toward the carrying capacity but never go beyond this limiting value. The following table shows additional data on paramecium cells.

$t$	$12$	$13$	$14$	$15$	$16$	$17$	$18$	$19$	$20$
$N$	$610$	$513$	$593$	$557$	$560$	$522$	$565$	$517$	$500$

a. Add these data to the graph in part b of Exercise 13.

b. Comment on the relationship of the data to the carrying capacity.

Paramecium Cells The following table is adapted from a paramecium culture experiment conducted by Cause in $1934$. The data show the paramecium population N as a function of time t in days.

$T$	$2$	$3$	$5$	$6$	$8$	$9$	$10$	$11$
$N$	$14$	$34$	$94$	$189$	$330$	$416$	$507$	$580$

a. Use regression to find a logistic model for this population.

b. Make a graph of the model you found in part a.

c. According to the model you made in part a, when would the population reach 450?