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MATH 1030-Homework 10: Linear Equations and Functions, Assignments of Mathematics

University of Utah (The U)Mathematics

Instructions and problems for homework #10 in math 1030, focusing on developing linear equations and functions. The problems involve analyzing the relationship between the number of violent crimes in san francisco, the average size of computers, and the population of an ant colony, as well as calculating the volume and surface area of various shapes.

Typology: Assignments

Pre 2010

Uploaded on 08/31/2009

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MATH 1030-003
Homework #10
Instructions: Do the following problems on a separate sheet of paper.
1. There were 10,937 violent crimes committed in San Francisco in 1994 and 7409 violent crimes committed
in 1998. It may or may not be a coincidence that these years are the exact years that Barry Bonds won
Gold Gloves and Silver Sluggers while playing for the San Francisco Giants.
(a) Develop a linear equation describing the number of violent crimes in San Francisco as a function of the
year.
(b) According to your equation, how many violent crimes were committed in San Francisco in 1995?
(c) If Barry Bonds hadn’t injured his elbow in 1999, use your linear equation to determine the year in which
there would have been only 5000 violent crimes.
2. The following (made-up) table describes the correlation between the average size of computers in cubic
feet and the global land surface temperature in degrees Fahrenheit.
computer size 4 2 1 .5
global temp 40.6 42.6 43.6 44.1
(a) Find a linear equation that describes the global land surface temperature as a function of the average
size of computers.
(b) According to your function, how large are computers when the global land surface temperature is 42.9?
(c) According to your function, how warm will the earth be when computers are one-tenth of a cubic foot?
3. The population of Petunia’s ant colony increases by 19 every 4 weeks. Suppose the population today is
449.
(a) Find a linear equation that describes the population of Petunia’s ant colony as a function of time in
weeks.
(b) Use your equation to predict how many ants Petunia will have in 11 weeks from now.
(c) Use your equation to find how long ago Petunia had only 100 ants.
4. A model spaceship has a volume of 42 cm3, a surface area of 62 cm2and a length of 50 cm. If the real
spaceship is 15000 cm long, find the volume and the surface area of the real spaceship.
5. A cylindrical tank has a height of 42 feet, a width of 50 feet, a surface area of 6,597.3 square feet, and
a volume of 82,466.8 cubic feet. If we want to make a scale model of the tank that is 3 feet tall, find the
width, the surface area, and the volume of the desired scale model.

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MATH 1030-

Homework #

Instructions: Do the following problems on a separate sheet of paper.

  1. There were 10,937 violent crimes committed in San Francisco in 1994 and 7409 violent crimes committed in 1998. It may or may not be a coincidence that these years are the exact years that Barry Bonds won Gold Gloves and Silver Sluggers while playing for the San Francisco Giants.

(a) Develop a linear equation describing the number of violent crimes in San Francisco as a function of the year.

(b) According to your equation, how many violent crimes were committed in San Francisco in 1995?

(c) If Barry Bonds hadn’t injured his elbow in 1999, use your linear equation to determine the year in which there would have been only 5000 violent crimes.

  1. The following (made-up) table describes the correlation between the average size of computers in cubic feet and the global land surface temperature in degrees Fahrenheit. computer size 4 2 1. global temp 40.6 42.6 43.6 44.

(a) Find a linear equation that describes the global land surface temperature as a function of the average size of computers.

(b) According to your function, how large are computers when the global land surface temperature is 42.9?

(c) According to your function, how warm will the earth be when computers are one-tenth of a cubic foot?

  1. The population of Petunia’s ant colony increases by 19 every 4 weeks. Suppose the population today is

(a) Find a linear equation that describes the population of Petunia’s ant colony as a function of time in weeks.

(b) Use your equation to predict how many ants Petunia will have in 11 weeks from now.

(c) Use your equation to find how long ago Petunia had only 100 ants.

  1. A model spaceship has a volume of 42 cm^3 , a surface area of 62 cm^2 and a length of 50 cm. If the real spaceship is 15000 cm long, find the volume and the surface area of the real spaceship.
  2. A cylindrical tank has a height of 42 feet, a width of 50 feet, a surface area of 6,597.3 square feet, and a volume of 82,466.8 cubic feet. If we want to make a scale model of the tank that is 3 feet tall, find the width, the surface area, and the volume of the desired scale model.