The table shows the populations (in millions) of five countries in 2000 and the projected populations (in millions) for the year 2015. Let t = 0 correspond to 2000. Find the exponential growth or decay model for each country using Desmos. Use each model to predict the population of each country in 2030. To determine the regression equation, type the data in the table for a country in the first entry line (t = 0 corresponds to the year 2000); then, in the second entry line, type the equation y1 aebx1. Country 2000 2015 Exponential Growth or Decay Model Population in 2030 Bulgaria 7.8 6.9 Canada 31.1 35.1 China 1268.9 1393.4 United Kingdom 59.5 62.2 United States 282.2 325.5
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
- The table shows the populations (in millions) of five countries in 2000 and the projected populations (in millions) for the year 2015. Let t = 0 correspond to 2000. Find the exponential growth or decay model for each country using Desmos.
- Use each model to predict the population of each country in 2030. To determine the regression equation, type the data in the table for a country in the first entry line (t = 0 corresponds to the year 2000); then, in the second entry line, type the equation y1 aebx1.
|
Country |
2000 |
2015 |
Exponential Growth or Decay Model |
Population in 2030 |
|
Bulgaria |
7.8 |
6.9 |
||
|
Canada |
31.1 |
35.1 |
||
|
China |
1268.9 |
1393.4 |
||
|
United Kingdom |
59.5 |
62.2 |
||
|
United States |
282.2 |
325.5 |
- It is evident that the populations of the United States and the United Kingdom are growing at different rates. What constant in the equation y = aebt is determined by these different growth rates? Discuss the relationship between the different growth rates and the magnitude of the constant.
|
Answer: |
Given that the exponential model is represented as y = a ebx , And the population of five countries is given as in the table and t = 0 correspond to 2000.
here the objective is to find the exponential growth or decay model by using the table
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