The U.S. Bureau of the Census prediction for the percentage of the population 65 years and older can be modeled as p(x) = −0.00022x3 + 0.014x2 − 0.0033x + 12.236 percent where x is the number of years since 2000, data from 0 ≤ x ≤ 50. 1. Determine the value of x in the domain 0 ≤ x ≤ 50 for which the percentage is predicted to be increasing most rapidly (Round your answer to three decimal places). 2. Thus, in which year is the percentage is predicted to be increasing most rapidly? 3. Calculate the percentage at that time. (Round your answer to two decimal places.) 4. Calculate the rate of change of the percentage at that time. (Round your answer to three decimal places.)
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 U.S. Bureau of the Census prediction for the percentage of the population 65 years and older can be modeled as
where x is the number of years since 2000, data from 0 ≤ x ≤ 50.
1. Determine the value of x in the domain 0 ≤ x ≤ 50 for which the percentage is predicted to be increasing most rapidly (Round your answer to three decimal places).
2. Thus, in which year is the percentage is predicted to be increasing most rapidly?
3. Calculate the percentage at that time. (Round your answer to two decimal places.)
4. Calculate the rate of change of the percentage at that time. (Round your answer to three decimal places.)
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