## Assignment: Growth Models Problem Set

Growth Models Problem Set

Fertility Dataset: Azerbaijan

Fertility Dataset: India

Fertility Dataset: United States

Life Expectancy Dataset: Bahrain

Life Expectancy Dataset: Finland

Life Expectancy Dataset: Namibia

### Skills

For each of the data sets presented in questions 1—6 below, complete the following using a spreadsheet:

(A) Enter the data into a table.

(B) Create a scatterplot.

(C) Select either a linear or an exponential trendline for the data according to the R-squared value. Report the R2 value and the equation of the trendline. If more than one type of equation could be used, select one and state your reasons for choosing it. State, if the data is not well-approximated by a linear or exponential trendline what, if any, model is a good fit.

(D) Use the trendline equation to make a prediction about the data.

Global fertility rates have generally decreased since 1960, having fallen from a high of approximately 5 births per woman in 1964 to approximately 2.4 births per woman in 2017. Use data from worldbank.org for the following countries to analyze trendlines in fertility rates by completing the five tasks given above for each of the following three datasets:

As global fertility rates have decreased, global life expectancy at birth has generally increased over the same time period (1960 to 2017), from an average of about 53 years in 1960 to about 72 years in 2017. Using the data from worldbank.org, complete the five tasks given above for each of the following three datasets:

### Extension of Module 8 Growth Models: Using function notation and spreadsheets

In the Module 8: Growth Models Problem Set questions #1 – 15, you wrote recursive and explicit formulas for given situations. Complete the following for questions #7 – 21 below, in which each situation presented previously in Module 8 has been rewritten from a function perspective as needed:

(A) Determine if the situation describes linear or exponential growth.

(B) Write a linear or exponential function that models the situation using the given information.

(C) Using a spreadsheet, build a model to make predictions.

1. a) Store the formula in cells.
2. b) Use the formula to make predictions about the situation given certain input.
3. c) write a new formula that will predict an input for a particular output.
4. Marko currently has 20 tulips in his yard. Each year he plants 5 more. How many tulips will he have planted in 7 years? How many years will it take for Marko to have planted at least 113 tulips?
5. Pam is a Disc Jockey. Every week she buys 3 new albums to keep her collection current. She currently owns 450 albums. How many albums will Pam have 12 years from now? How many years from now will it take for Pam to have at least 500 albums in her collection?
6. In the year 2010 a certain store had annual sales of $40,000. Over the next 5 years, the sales grew by$15,000 per year. If this trend continues, what will the store’s annual sales be in the year 2020? In what year did the store’s sales exceed $100,000? 7. There were 200 houses in a certain town in the year 1997. The number of houses increased on average by 30 houses per year during the next five years. If the trend were to continue, how many houses would there be in the town in the year 2007? In what year would the number of houses have reached at least 400? 8. A population of beetles is growing according to a linear growth model. In the first week of observation (week 0), there were 3 beetles. The population after 8 weeks is 67. Write a linear equation in slope-intercept form that will predict the number of beetles in the population in week n. How many weeks will it take for the population to reach 187 beetles? 9. The number of streetlights in a town is growing linearly. Four months ago (n = 0) there were 130 lights. Now (n = 4) there are 146 lights. Assuming the trend continues, write a linear equation in slope-intercept form that will predict the number of lights in month n. How many months will it take to reach 200 lights? 10. Tacoma’s population in the year 2000 was about 200 thousand and had been growing by about 9% each year. If the trend continues, what will the population of Tacoma be in 2016? In what year would the population exceed 400 thousand? 11. Portland’s population in 2007 was about 568 thousand, and had been growing by about 1.1% each year. If this trend continues, what will Portland’s population be in 2016? In what year will Portland’s population reach 700 thousand? 12. Diseases tend to spread according to the exponential growth model. In the early days of AIDS, the growth rate was around 190%. In 1983, about 1700 people in the U.S. died of AIDS. If the trend had continued unchecked, how many people would have died from AIDS in 2005? In what year would the number of deaths have reached 25,000? 13. The population of the world in 1987 was 5 billion and the annual growth rate was estimated at 2 percent per year. Assuming that the world population follows an exponential growth model, find the projected world population in 2015. Under this model? in what year would the world population would have reached 10 billion? (The population growth rate was at a peak between 1950 and 1987. It has since declined to about 1.2% in 2017 and predicted to decline further. World population in 2019 was estimated to be 7.6 billion. Source: https://www.census.gov/popclock/ ) 14. A bacteria culture is started with 300 bacteria. After 4 hours, the population has grown to 500 bacteria. If the population grows exponentially and this trend continues, how many bacteria will there be in 1 day? How long does it take for the culture to triple in size? 15. A native wolf species has been reintroduced into a national forest. Originally 200 wolves were transplanted. After 3 years, the population had grown to 270 wolves. If the population grows exponentially, and if this trend continues, how many wolves will there be in 10 years? How long will it take the population to grow to 1000 wolves? 16. One hundred trout are seeded into a lake. Absent constraint, their population will grow by 70% a year. The lake can sustain a maximum of 2000 trout. Using the logistic growth model, determine how many fish will be in the lake 2 years after it was seeded. How long will it take for there to be 1000 trout in the lake? 17. Ten blackberry plants started growing in my yard. Absent constraint, blackberries will spread by 200% a month. My yard can only sustain about 50 plants. Using the logistic growth model, determine how many plants will be in my yard after 1, 2, 3, 4, and 5 months. What appears to be happening to the number of plants in the yard over time? 18. In 1968, the U.S. minimum wage was$1.60 per hour. In 1976, the minimum wage was $2.30 per hour. Assume the minimum wage grows according to an exponential model where n represents the time in years after 1960. What does the model predict for the minimum wage in 1960? If the minimum wage was actually$5.15 in 1996, is this above, below or equal to what the model predicts?