1. 1 st Saturday Sections 1.5, 1.8 – 1.11, 2.1

2. Apple first introduced the iPod in 2006. Since then, sales of the iPod can be modeled by million units x years after 2006. (a)By what percentage were iPod sales growing after first being introduced? (b)According to the model, what were iPod sales in the year 2008? Example 1

3. In 1900 the world population was about 1.6 billion people. It has been growing fairly constantly at a rate of 1.4% per year since then. (a)Let x represent the number of years since 1900, and construct a model for the world population. (b)What is the predicted world population for this year? Example 2

4. Tritium is a radioactive form of hydrogen, and it decays at a rate of 5.5% per year. Suppose there are 50 grams of tritium in a container initially. (a)Give a model for the amount of tritium remaining after y years. (b)How much tritium remains after 18 months? (a)What is the half-life of tritium? Example 3

5. The table below below gives the national health care costs, measured in billions of dollars, in various years. (a)Let x = # years since 1970, look at a scatterplot of the data, discuss the features that make an exponential model appropriate, and then find the model. (b)What was the constant percentage change during this time span? Example 4 Year19701980199020002010 Cost7525371413532570

6. The table gives measurements of atmospheric pressure, measured in grams per cm 2, at various altitudes, measured in km. (a)Find an exponential model for this data. (b)What is the constant percentage change in atmospheric pressure? (c)Estimate the atmospheric pressure at an altitude of 11.8km. Example 5 Altitude510152025 Pressure5693131729552

7. The table shows the number of homes (in millions) having Cable TV in various years. (a)Let x be the years since 1980, examine a scatterplot of the data and then find an appropriate model. (b)Based on the model, how many homes had Cable TV in 1986? Example 6 Year198119831985198719891991 # Homes2.46.48.379.6210.5511.3

8. The table shows the minimum temperature (in °F) at which milk must be stored so that it will stay fresh for x days. (a)Examine a scatterplot of the data and then find an appropriate model. (b)Based on the model, at what temperature will milk stay fresh for one week? Example 7 Days0.51251024 Temp.706050453830

9. The table gives the average fuel consumption (in gallons per vehicle) in the U.S. for various years. (a)Choose a reasonable alignment for the input variable and find the most appropriate model for this data. (b)Estimate the fuel consumption in 1992. Example 8 Year197019751980198519901995 Consumption830775712685677700

10. The table gives the number of roofing jobs a certain company had in various months of last year. (a)Choose a reasonable alignment for the input variable and find the most appropriate model for this data. (b)According to the model, how many jobs did this company have in April of last year? Example 9 MonthJan.MarchMayJuly # Jobs122258117

11. The table shows the profit a certain company makes from the sale of x blenders. (a)Find the most appropriate model for this data. (b)According to the model, what is the profit when 12 blenders are sold? (c)Why should we not use the model to predict profit if 30 blenders are sold? Example 10 x47101316 Profit ($)114247356418451

12. The table shows the number of men (from a group of 200) that were taller than x inches. (a)Find the most appropriate model for this data. (b)According to the model, how many of these men were taller than 68.5 inches? Example 11 x656769717375 # Men19818413971264

13. The table shows the total number of people in a small town that subscribed to a new magazine x weeks after it had first been released. (a)Find the most appropriate model for this data. (b)According to the model, how many people had subscriptions for this magazine after 18 weeks? Example 12 x51015202530 # people9930066398511331181

14. The table shows the average price of natural gas (measured in dollars per 1000ft 3 ) for residential use in the U.S. for various years. (a)Choose an appropriate alignment for x and then find the most appropriate model for this data. (b)What was the price in 1988? Example 13 Year1980198219851990199519961997 Price3.685.176.125.776.066.346.93

15. The number of deer, N, on a wildlife preserve x years after the herd was first introduced is modeled by the formula: (a)Find and interpret the change in the number of deer between years 4 and 10. (b)Find and interpret the percent change in the number of deer between years 2 and 8. (c)Find and interpret the average rate of change in the number of deer between years 1 and 6. Example 14

16. The table shows the number temperature (in °F) on a typical May day in a mid-western city at various times. (a)Find and interpret the average rate of change in the temperature between 8:30am and noon. (b)Find and interpret the percent change in temperature between 12:45pm and 6pm. Example 15 Time7am9am11am1pm3pm5pm Temp.496676807869