59.Forensic scientists use the lengths of certain bones to calculate the
height of a person. Two bones often used are the tibia , the bone
from the ankle to the knee, and the femur , the bone from the knee
to the hip socket. A person’s height in centimeters is determined
from the lengths of these bones by using functions defined by the fol-
lowing formulas.
For men: or
For women: or
(a)Find the height of a man with a femur measuring 56 cm.
(b)Find the height of a man with a tibia measuring 40 cm.
(c)Find the height of a woman with a femur measuring 50 cm.
(d)Find the height of a woman with a tibia measuring 36 cm.
60.Federal regulations set standards for the
size of the quarters of marine mammals. A
pool to house sea otters must have a volume
of “the square of the sea otter’s average
adult length (in meters) multiplied by 3.14
and by 0.91 meter.” If xrepresents the sea
otter’s average adult length and repre-
sents the volume (in cubic meters) of the
corresponding pool size, this formula can
be written as
.
Find the volume of the pool for each adult sea otter length (in meters). Round answers to
the nearest hundredth.
(a)0.8 (b)1.0 (c)1.2 (d)1.5
61.To print t-shirts, there is a $100 set-up fee, plus a $12 charge per t-shirt. Let xrepresent
the number of t-shirts printed and represent the total charge.
(a)Write a linear function that models this situation.
(b)Find. Interpret your answer in the context of this problem.
(c) Find the value of xif Express this situation using function notation,
and interpret it in the context of this problem.
62.Rental on a car is $150, plus $0.20 per mile. Let xrepresent the number of miles driven
and represent the total cost to rent the car.
(a)Write a linear function that models this situation.
(b)How much would it cost to drive 250 mi? Interpret this question and answer, using
function notation.
(c) Find the value of xif Interpret your answer in the context of this
problem.
63.The table represents a linear function.
(a)What is?
(b)If , what is the value of x?
(c) What is the slope of the line?
(d)What is the y-intercept of the line?
(e) Using your answers from parts (c) and (d), write
an equation for ƒ 1 x 2.
ƒ 1 x 2 =-2.5
ƒ 122
ƒ 1 x 2 =230.
ƒ 1 x 2
ƒ 1 x 2 =1000.
ƒ 11252
ƒ 1 x 2
ƒ 1 x 2 =0.91 1 3.14 2 x^2
ƒ 1 x 2
h 1 r 2 =61.41+2.32r h 1 t 2 =72.57+2.53t
h 1 r 2 =69.09+2.24r h 1 t 2 =81.69+2.39t
1 h 2
1 r 2
1 t 2
196 CHAPTER 3 Graphs, Linear Equations, and Functions
Tibia
Femur
x
0 3.5
1 2.3
2 1.1
3 0.1
4 1.3
5 - 2.5
y=ƒ 1 x 2
