Title: Nonlinear Models
Course: Question Banks

Q: The population of Australia in 2010 was approximately 22.4 million. Its growth rate is projected to be 1.5% per year.

Based on these assumptions, which of the following is an exponential model of the population of Australia from the year 2010? (Let t = number of years after 2010 and y = population of Australia in millions.)
- y = 22.4 (1.15)^t (This model shows a 15% growth rate, not a 1.5% growth rate.)
- y = 22.4 (0.015)^t (Think about the growth factor as 100% + a percent increase.)
- y = 22.4 (1.15)t (This model is linear with a slope of 22.4 (1.15). It is not an exponential model.)
- y = 22.4 (1.015)^t (1.5% growth is a growth factor of 1.015.)
A: y = 22.4 (1.015)^t

Q: A minor league baseball team did a study on attendance at their ballpark. The growth in game attendance was exponential. The model y = 5000 (1.034)^t, where y is the predicted attendance and t is the years from 2000, fits the data.

Which statement below is most accurate about the ballpark’s attendance?
- Baseball attendance is growing yearly by 34%. (You chose 34% growth. This is a growth factor of 1.34. The growth factor in the model is 1.034. Think of this as a percent: 103.4%. What is the percent increase?)
- Baseball attendance is growing yearly by 134%. (You chose 134% growth. This is a growth factor of 2.34. The growth factor in the model is 1.034. Think of this as a percent: 103.4%. What is the percent increase?)
- Baseball attendance is growing yearly by 0.034%. (The growth factor for your choice comes from 100% + 0.034% = 100.034%. So the growth factor for your answer is 1.00034. The growth factor in the model is 1.034. Think of this as a percent: 103.4%. What is the percent increase?)
- Baseball attendance is growing yearly by 3.4%. (The growth factor is 1.034. Think of this as a percent: 103.4%. This is 3.4% growth.)
A: Baseball attendance is growing yearly by 3.4%.

Q: Which of the following models does NOT represent a negative association?
- y = 20 – (0.85)t (This equation does model a negative association. This is a linear model with a negative slope. So, y will decrease as t increases.)
- y = 20 (0.85)^t (This equation does model a negative association. Multiplying by a factor of 0.85 decreases the original amount by 15%.)
- y = 20 + (0.85)t (This equation models a positive association. This is a linear model with a positive slope. So, y will increase as t increases.)
A: y = 20 + (0.85)t

Q: With the growing popularity of cell phones, a local phone company had a sharp decline in the number of customers with land-line phones in their homes. Suppose land-line phones are decreasing at a rate of 27% each year since 2000. Assume that there were 10,000 subscribers with land-line phones in the year 2000.

For convenience let t = the number of years after 2000 and y = number of subscribers with land-line phones.

A formula that models this scenario is:
- y = 2000 (0.73)^t (You’ve chosen the correct decay factor, but your initial value is incorrect.)
- y = 10,000 (1.27)^t (This model predicts that the amount is growing at a rate of 27% each year. Instead, we want the amount to decline.)
- y = 10,000 (0.27)^t (You’ve chosen the correct initial value but your decay factor is incorrect. A decline of 27% means 73% remains.)
- y = 10,000 (0.73)^t (A decline of 27% each year means 73% remains. The initial value is 10,000.)
A: y = 10,000 (0.73)^t