2.8 Fitting Models to Curved Relationships

In a fascinating study about the pace of life, M.H. Bernstein was able to show a positive relationship between the average walking speed of pedestrians in 15 cities around the world and the population size of cities. We calculated the quadratic and exponential models to predict y = city size from x = walking speed. Based on the residual plots, which model is more appropriate?

• 
• 

Tags

CCSS.HSS.ID.B.6B

The average salary of Major League Baseball players has been growing very rapidly since 1970. A quadratic model & an exponential model were calculated to predict y = average salary from x = years since 1970. Based on the residual plots, which model is more appropriate?

• 
• 

Many populations grow exponentially. Here are the data for the estimated population of Europe (in millions) from 1700 to 2012. The dates are recorded as years since 1700 so that x = 312 is the year 2012. Calculate an EXPONENTIAL model for these data using years since 1700 as the explanatory variable.

• 
• 
• 
• 

Tags

CCSS.HSF.LE.A.2

Expose marine bacteria to X-rays for time periods from 1 to 15 minutes. Here are the number of surviving bacteria (in hundreds) on a culture plate after each exposure time. Calculate an EXPONENTIAL model for these data using time as the explanatory variable.

• 
• 
• 
• 

Tags

CCSS.HSF.LE.A.2

A student opened a bag of M&M's Chocolate Candies, dumped them out, and ate all the ones with the "M" on top. When he finished, he put the remaining 30 M&M's back in the bag and repeated the same process over and over until all the M&M's were gone. Here are data on the number of M&M's remaining at the end of each of the first 6 courses. Calculate an EXPONENTIAL model for these data using course as the explanatory variable.

• 
• 
• 
• 

Tags

CCSS.HSF.LE.A.2

The table gives the price (in dollars) and weight (in carats) for 15 randomly selected round, clear, internally flawless diamonds with excellent cuts. Calculate a QUADRATIC model for these data using carat weight as the explanatory variable.

• 
• 
• 
• 

A team of researchers measured the carapace (shell) length and clutch size (number of eggs) for female gopher tortoises in Okeeheelee County Park, Florida. Here are the data for 16 tortoises. Calculate a QUADRATIC model for these data using carapace length as the explanatory variable.

• 
• 
• 
• 

Hall-of-Fame pitcher Bob Gibson of the St. Louis Cardinals was one of the most dominant pitchers during the 1960s. The table shows his age and WHIP (walks & hits per inning pitched) for each year of his career, beginning in 1959. Calculate a QUADRATIC model for these data using age as the explanatory variable.

• 
• 
• 
• 

Fuel efficiency for many cars is related to how fast the car is driven. To explore this relationship, some researchers calculated the mean fuel efficiency for nine different car models at 13 different speeds. Here are the results. Calculate a quadratic model for these data using speed as the explanatory variable.

• 
• 
• 
•