Fertility Dataset: United States
Life Expectancy Dataset: Bahrain
Life Expectancy Dataset: Finland
Life Expectancy Dataset: Namibia
Directions for questions 1-6:
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.
Scenario for questions 1-6:
Global fertility rates have generally decreased since 1960, having fallen from a high of approximately [latex]5[/latex] births per woman in 1964 to approximately [latex]2.4[/latex] births per woman in 2017. Use data from worldbank.org for the following countries to analyze trendlines in fertility rates by completing the four tasks given above for each of the following three datasets:
| 1. India | 2. The United States | 3. Azerbaijan |
| Fertility Dataset: India | Fertility Dataset: United States | Fertility Dataset: Azerbaijan |
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 [latex]53[/latex] years in 1960 to about [latex]72[/latex] years in 2017. Using the data from worldbank.org, complete the four tasks given above for each of the following three datasets:
| 4. Bahrain | 5. Finland | 6. Namibia |
| Life Expectancy Dataset: Bahrain | Life Expectancy Dataset: Finland | Life Expectancy Dataset: Namibia |
- Marko currently has [latex]20[/latex] tulips in his yard. Each year he plants [latex]5[/latex] more. How many tulips will he have planted in [latex]7[/latex] years? How many years will it take for Marko to have planted at least [latex]113[/latex] tulips?
- Pam is a Disc Jockey. Every week she buys [latex]3[/latex] new albums to keep her collection current. She currently owns [latex]450[/latex] albums. How many albums will Pam have [latex]12[/latex] years from now? How many years from now will it take for Pam to have at least [latex]500[/latex] albums in her collection?
- In the year 2020 a certain store had annual sales of [latex]$40,000[/latex]. Over the next [latex]5[/latex] years, the sales grew by [latex]$15,000[/latex] per year. If this trend continues, what will the store’s annual sales be in the year 2030? In what year did the store’s sales exceed [latex]$100,000[/latex]?
- There were [latex]200[/latex] houses in a certain town in the year 1997. The number of houses increased on average by [latex]30[/latex] 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 [latex]400[/latex]?
- A population of beetles is growing according to a linear growth model. In the first week of observation (week 0), there were [latex]3[/latex] beetles. The population after [latex]8[/latex] weeks is [latex]67[/latex]. 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 [latex]187[/latex] beetles?
- The number of streetlights in a town is growing linearly. Four months ago (n = 0) there were [latex]130[/latex] lights. Now (n = 4) there are [latex]146[/latex] 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 [latex]200[/latex] lights?
- Tacoma’s population in the year 2000 was about [latex]200[/latex] thousand and had been growing by about [latex]9\%[/latex] each year. If the trend continues, what will the population of Tacoma be in 2016? In what year would the population exceed [latex]400[/latex] thousand?
- Portland’s population in 2007 was about [latex]568[/latex] thousand, and had been growing by about [latex]1.1\%[/latex] each year. If this trend continues, what will Portland’s population be in 2016? In what year will Portland’s population reach [latex]700[/latex] thousand?
- The population of the world in 1987 was [latex]5[/latex] billion and the annual growth rate was estimated at [latex]2[/latex] 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 [latex]10[/latex] billion? (The population growth rate was at a peak between 1950 and 1987. It has since declined to about [latex]1.2\%[/latex] in 2017 and predicted to decline further. World population in 2019 was estimated to be [latex]7.6[/latex] billion. Source: https://www.census.gov/popclock/ )
- A bacteria culture is started with [latex]300[/latex] bacteria. After [latex]4[/latex] hours, the population has grown to [latex]500[/latex] bacteria. If the population grows exponentially and this trend continues, how many bacteria will there be in [latex]1[/latex] day? How long does it take for the culture to triple in size?
- A native wolf species has been reintroduced into a national forest. Originally [latex]200[/latex] wolves were transplanted. After [latex]3[/latex] years, the population had grown to [latex]270[/latex] wolves. If the population grows exponentially, and if this trend continues, how many wolves will there be in [latex]10[/latex] years? How long will it take the population to grow to [latex]1000[/latex] wolves?
- One hundred trout are seeded into a lake. Absent constraint, their population will grow by [latex]70\%[/latex] a year. The lake can sustain a maximum of [latex]2000[/latex] trout. Using the logistic growth model, determine how many fish will be in the lake [latex]2[/latex] years after it was seeded. How long will it take for there to be [latex]1000[/latex] trout in the lake?
- Ten blackberry plants started growing in my yard. Absent constraint, blackberries will spread by [latex]200\%[/latex] a month. My yard can only sustain about [latex]50[/latex] plants. Using the logistic growth model, determine how many plants will be in my yard after [latex]1[/latex], [latex]2[/latex], [latex]3[/latex], [latex]4[/latex], and [latex]5[/latex] months. What appears to be happening to the number of plants in the yard over time?
- In 1968, the U.S. minimum wage was [latex]$1.60[/latex] per hour. In 1976, the minimum wage was [latex]$2.30[/latex] 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 [latex]$5.15[/latex] in 1996, is this above, below or equal to what the model predicts?