32 Chapter P: Preparation for Calculus
P.4 Fitting Models to Data
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Determine which type of function would be most appropriate to fit the given data.
a. exponential
b. linear
c. quadratic
d. no relationship
e. trigonometric
P.4 Fitting Models to Data 33
____ 2. Which function below would be most appropriate model for the given data?
a. no apparent relationship between x and y
b. trigonometric
c. quadratic
d. linear
____ 3. Hooke’s Law states that the force F required to compress or stretch a spring (within
its elastic limits) is proportional to the distance d that the spring is compressed or stretched from its
original length. That is, where k is a measure of the stiffness of the spring and is called the
spring constant. The table shows the elongation d in centimeters of a spring when a force of F
newtons is applied. Use the regression capabilities of a graphing utility to find a linear model for the
data. Round the numerical values in your answer to three decimal places.
a.
b.
c.
d.
e.
34 Chapter P: Preparation for Calculus
____ 4. Hooke’s Law states that the force F required to compress or stretch a spring (within
its elastic limits) is proportional to the distance d that the spring is compressed or stretched from its
original length. That is, where k is a measure of the stiffness of the spring and is called the
spring constant. The table shows the elongation d in centimeters of a spring when a force of F
newtons is applied. Use a graphing utility to plot the data and graph the linear model.
a. d.
b. e.
P.4 Fitting Models to Data 35
c.
____ 5. Hooke’s Law states that the force F required to compress or stretch a spring (within
its elastic limits) is proportional to the distance d that the spring is compressed or stretched from its
original length. That is, where k is a measure of the stiffness of the spring and is called the
spring constant. The table shows the elongation d in centimeters of a spring when a force of F
newtons is applied. Use the model to estimate the elongation of the spring when a force
of 55 newtons is applied. Round your answer to two decimal places.
a. 8.08 cm
b. 6.38 cm
c. 4.68 cm
d. 2.98 cm
e. 9.78 cm
____ 6. In an experiment, students measured the speed s (in meters per second) of a falling
object t seconds after it was released. The results are shown in the table below. Use the regression
capabilities of a graphing utility to find a linear model for the data. Round all numerical values in
your answer to one decimal place.
a.
b.
c.
d.
e.
36 Chapter P: Preparation for Calculus
____ 7. In an experiment, students measured the speed s (in meters per second) of a falling
object t seconds after it was released. The results are shown in the table below. Use the regression
capabilities of a graphing utility to find a linear model for the data. Round all numerical values in
your answer to one decimal place.
a. d.
b. e.
P.4 Fitting Models to Data 37
c.
____ 8. In an experiment, students measured the speed s (in meters per second) of a falling
object t seconds after it was released. The results are shown in the table below. Use the model
to estimate the speed of the object after seconds. Round your answer to two
decimal places.
a. 21.05 meters/second
b. 20.95 meters/second
c. 24.25 meters/second
d. 23.55 meters/second
e. 22.65 meters/second
____ 9. Students in a lab measured the breaking strength S (in pounds) of wood 2 inches
thick, x inches high, and 12 inches long. The results are shown in the table below. Use the regression
capabilities of a graphing utility to fit a quadratic model to the data. Round the numerical values in
your answer to two decimal places, where applicable.
a.
b.
c.
d.
e.
38 Chapter P: Preparation for Calculus
____ 10. Students in a lab measured the breaking strength S (in pounds) of wood 2 inches
thick, x inches high, and 12 inches long. The results are shown in the table below. Use a graphing
utility to plot the data and graph the quadratic model.
a. d.
b. e.
P.4 Fitting Models to Data 39
c.
____ 11. Students in a lab measured the breaking strength S (in pounds) of wood 2 inches
thick, x inches high, and 12 inches long. The results are shown in the table below. Use the model
to approximate the breaking strength when . Round your answer
to two decimal places.
a. 595.98 pounds
b. 390.19 pounds
c. 957.76 pounds
d. 801.77 pounds
e. 751.97 pounds
____ 12. A V8 car engine is coupled to a dynamometer and the horsepower y is measured at
different engine speeds x (in thousands of revolutions per minute). The results are shown in the table
below. Use the regression capabilities of a graphing utility to find a cubic model for the data. Round
the numerical values in your answer to three decimal places, where applicable.
a.
b.
c.
d.
e.
40 Chapter P: Preparation for Calculus
____ 13. A V8 car engine is coupled to a dynamometer and the horsepower y is measured at
different engine speeds x (in thousands of revolutions per minute). The results are shown in the table
below. Use a graphing utility to plot the data and graph the cubic model.
a. d.
b. e.
c.
P.4 Fitting Models to Data 41
____ 14. A V8 car engine is coupled to a dynamometer and the horsepower y is measured at
different engine speeds x (in thousands of revolutions per minute). The results are shown in the table
below. Use the model to approximate the horsepower when the
engine is running at 5500 revolutions per minute. Round your answer to two decimal places.
a. 260.77 hp
b. 262.73 hp
c. 262.36 hp
d. 261.38 hp
e. 261.91 hp
____ 15. The motion of an oscillating weight suspended by a spring was measured by a motion
detector. The data collected and the approximate maximum (positive and negative) displacements
from equilibrium are shown in the figure. The displacement is measured in centimeters, and the time
is measured in seconds. Take A(0.133,2.49) and B(0.343,1.78). Approximate the amplitude and
period of the oscillations.
a. Amplitude = 0.335. Period = 4.3.
b. Amplitude = 0.71. Period = 2.1.
c. Amplitude = 0.355. Period = 4.2.
d. Amplitude = 4.2. Period = 0.355.
e. Amplitude = 2.1. Period = 0.71.
42 Chapter P: Preparation for Calculus
P.4 Fitting Models to Data
Answer Section
MULTIPLE CHOICE