Chapter 5.1, Problem 12E

Special Rounding Instructions When you perform logistic regression, round the r value to three decimal places and the other parameters to two decimal places. Round all answers to two decimal places unless other-wise indicated.

Natural Gas Production The following table shows natural gas production N in trillions of cubic feet in the United states t years after $1940$.

$t=yearssince1940$	$N=cubicft.intrilliions$
$0$	$3.75$
$10$	$8.48$
$20$	$15.09$
$30$	$23.79$
$40$	$21.87$
$50$	$21.52$
$60$	$24.15$

a. Make a logistic model for N as a function of t.

b. Graph the data and the logistic model.

c. Which year's production was farthest from the prediction of the logistic model?

d. What does the logistic model predict for the amount of natural gas that will be produced in the long run? (Note: In other contexts, this would be known as the carrying capacity.).