Chapter 1: Polynomial Functions
Investigation 1.2—Motorcycles and Helmets
Did You Know?
If a vehicle equipped with an air bag experiences a hard impact, generally in excess of 10
miles per hour, a crash sensor sends an electronic signal that triggers an explosion. The
explosion generates nitrogen gas that inflates the air bags, and they burst from their
locations and inflate in less than one-tenth of a second. The air bag absorbs impact
energy by forcing gas out through a series of ports in the air bag fabric.
Reference: www.britannica.com/EBchecked/topic/44957/automobile
In the United States, each year the National Highway Traffic Safety Administration
(NHTSA) estimates the number of lives saved by different protective devices. The
following functions approximate the number of lives saved each year by airbags,
safety belts, and motorcycle helmets, where t = 0 represents 1990.
Airbags: L
A
= 0.0444t
4
+ 0.0362t
3
+ 22.361t
2
11.147t + 41.81
Safety-Belts: L
S
= 0.119t
5
+ 4.8727t
4
71.739t
3
+ 443.81t
2
321.73t + 6601.5
Motorcycle Helmets: L
H
= 0.0548t
4
+ 1.9586t
3
15.87t
2
+ 34.646t + 626.26
a.
Graph all three functions on the same xy-coordinate plane. For what domain
do you think these functions will provide accurate estimates of the lives saved
as a result of these safety devices?
b.
Find the y-intercepts of each function. What is the real-world meaning of the
y-intercepts? Explain.
c.
Do any of the functions have x-intercepts? Explain.
d.
Which of the protective devices save the most lives each year?
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