Chapter 4.4, Problem 24E

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.

Traffic in the Lincoln Tunnel Characteristics of traffic flow include density $D$, which is the number of cars per mile, and average speed $s$ in $\text{miles}\text{per}\text{hour}$.Traffic system engineers have investigated several methods for relating density to average speed. One study considered traffic flow in the north tube of the Lincoln Tunnel and fitted an exponential function to observed data. Those data are partially presented in the table below.

Speed $s$	Density $D$
$32$	$34$
$25$	$53$
$20$	$74$
$17$	$88$
$13$	$102$

a.Make an approximate exponential model of $D$ as a function of $s$.

b.Express, using functional notation, the density of traffic flow when the average speed is $28\text{mile}\text{per}\text{hour}$, and then calculate that density.

c.If average speed increases by $1\text{mile}\text{per}\text{hour}$, what can be said about density?