ART031

From "Can We Do Business With China?":

1. Find the slope of the line, including units.

2. What does the slope of the line mean in terms of the variables?

3. Write an equation that expresses U.S. - China trade as a function of time.

4. If the trend continues how much will the U.S. - China trade be in the year 2000?

5. If the trend continues when will the U.S. - China trade be $100 billion dollars?

6. What does the area under the line of best fit represent in terms of the variables?

7. Write an equation for the area under the line of best fit.

8. If the trend continues, how much will we have paid China from 1991 to 2000?

9. Sketch a graph of the equation for the area under the line of best fit.

ART032

From "Reeling in the Years":

1. Draw a graph of the data. Draw the curve of best fit.

2. Find a mathematical model that describes amount of time from an invention until a quarter of people in the United States use the new invention. Write the equation for the model.

3. Explain why you chose the model you did.

4. Predict the amount of time until a new invention invented in 2000 is used by a quarter of the people in the United States.

5. What factors could affect the accuracy of your prediction?

ART033

From "More War":

"It was a seminal week in the browser wars. Microsoft started freely distributing copies of Internet Explorer 4.0, which merges the roles of operating system and browser, delivering information (and ads) from the Internet right to the desktop. More than 1 million people downloaded the program. Meanwhile, Sun Microsystems filed a lawsuit against Microsoft, alleging that IE misuses its Java technology."

1. What would be the significance of adding these three graphs?

2. Explain the trends exhibited by these graphs.

3. Which line has the greatest positive slope? When? What does it mean?

4. Which has the greatest negative slope? When? What does it mean?

ART034

From an advertisement for LYMErix by SmithKline Beecham Pharmaceuticals for a vaccine for Lyme Disease:

Incidence of Unsolicited Adverse Events Occurring after Doses 1, 2, or 3

1. How many out of 100 persons who received Lyme disease vaccine may feel pain at the injection site?

2. How many out of 100 persons who received the placebo may feel pain at the injection site.

3. What is the probability that someone who receives a Lyme disease vaccine will have chills? Express your answer as a percent, decimal and fractions.

4. What is the probability a person who receives the vaccine will have chills or fatigue?

5. What is the probability a person who receives the vaccine will have chills and fatigue?

6. Which symptom seems to be the most indicative of having received the vaccine instead of a placebo? Explain.

ART035

From "Freeze Frame for Rentals":

1. Graph the data for Video Rentals vs. Time.

2. Graph the data for Video Sales vs. Time.

3. What type of function does Video Rentals vs. Time seem to be?

4. What type of function does Video Sales vs. Time seem to be?

5. Write an equation for Video Sales vs. Time.

6. Test your equation for 1993. How closely does your function match the data?

7. What factors could account for the differences in these two functions?

ART036

From "Yak! Yak! Yak!":

"The number of cell phones in use around the world is expected to more than double by 2002."

Cell Phone Subscribers in Millions

1. Assuming the function is exponential, what is the doubling time in 1998 for the number of cell phones in use around the world?

2. Write an exponential function based on the doubling time in 1998.

3. In which country is cell phone use growing the fastest?

4. Write an exponential function for cell phone use in the country where it is growing the fastest.

5. What is the growth rate for cellular phone use in the world? Express your answer as a decimal and as a percent.

6. Based on your exponential model, predict the number of cell phones that will be in use in the world in 2050?

7. What factors might change your prediction?

ART037

From "The Y2K Watch":

1. Graph the data and draw the curve of best fit.

2. Find an equation that expresses Cost per line of code corrected over time.

4. Find the rate of change of the function. Express your answer as a decimal and as a percent.

5. Assuming the trend continues, find the cost per line of code in 1993.

6. What does the vertical intercept of the function represent?

ART038

From "The Little Spacecraft That Could":

"The radius of the moon as a whole is 1,738 kilometers. Lunar Prospector's magnetometer was able to measure the weak field induced in the moon's core when the body passed through the tail of Earth's magnetosphere. From these data, the scientists calculated a core radius of between 300 and 425 kilometers. At this size, the moon's core would contain only about 2 percent of the body's mass. In contrast, Earth's core, which has a radius of about 3,400 kilometers, comprises about 30 percent of the planet's mass."

1. What is the volume of the moon?

2. What is the volume of the moon's core?

3. If the radius of the earch is 6.37 x 10⁶ meters what is the volume of the Earth?

4. What is the volume of the Earth's core

3. What percent of the volume of the moon is in its core?

4. What percent of the Earth's volume is in its core?

5. If the mass of the moon is 7.34 x 10²² kilograms what is the mass of the moon's core?

6. If the mass of the Earth is 5.98 x 10²⁴ kilograms what is the mass of the Earth's core?

7. Density is mass divided by volume. Is the density of the Earth's or the moon's core closest to the density of iron? (The density of iron is 7.4 grams/cubic centimeter ).

ART039

From "A Probing Prelude":

"Global Surveyor's laser altimeter contributed an important finding about the planet's northern polar ice cap. Scientists had long assumed that this cap held a significant amount of Mars's water. But the altimeter showed that it in fact contains no more than about 1.2 million cubic kilometers of ice."

1. The radius of Mars is 2100 miles. If all the ice in the ice cap were melted, the water would cover Mars to what average depth?

ART040

From "Nation of Deadbeats?":

1. Graph the data and draw the curve of best fit.

2. Write an exponential equation for U.S. bankruptcy filings as a function of time.

3. What is the growth rate for U.S. bankruptcy filings? Express your answer as a decimal and as a percent.

6. Based on your exponential model, predict the number of U.S. bankrupcy filings in the year 2000?

7. If the trend continues when will the number of U.S. bankruptcy filings be 2 million?

8. What factors might change your prediction?

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Copyright © 1999 [Shay Cardell]. All rights reserved.
Revised: July 31, 1999 .