A table of the U.S. population in millions indicated in 1960 the population was 181 million, in 1970 the population was 205 million, in 1980 the population was 228 million, and in 1990, the population was 250 million.
Describe the context behind how the functions are being used. Identify the domain and range of each function you found. Include any charts or graphs that will help explain the functions you found.
and your thinking is what?
domain is the x value which is years and changes in the population are the numbers in millions. I am having a problem setting the problem up. I think it is..
g(x)1/x-3
In the given information, a table is provided which shows the U.S. population in millions for the years 1960, 1970, 1980, and 1990. The table displays the population count for each year mentioned.
To find the functions that describe the population growth over these years, we can use regression analysis. Regression analysis helps us find the relationship between two or more variables, in this case, time (years) and population count.
To begin, let's assign the year as the independent variable (x) and the population count as the dependent variable (y). We can then plot the data points on a chart or graph to visualize the trend.
Let's create a scatter plot for the given data:
Year (x) | Population (y)
--------------------------------------------------
1960 | 181
1970 | 205
1980 | 228
1990 | 250
Now, plot these points on a graph. The x-axis should represent the years, and the y-axis should represent the population count.
Once the points are plotted, we can see that they form a fairly linear pattern. This suggests that there is a linear relationship between the year (x) and the population count (y).
Now, we can use the method of least squares regression to find the equation of the line that best fits these data points. By fitting a line to the scatter plot, we can establish a mathematical relationship between the year and the population count.
The equation of a linear function is y = mx + b, where m is the slope of the line and b is the y-intercept.
Using regression analysis, we can find the values of m and b that best fit the data points.
Once we find the values, we can write the equation of the function that describes the population growth over time for the given data. This equation will represent a linear function in the form of y = mx + b.
To find the domain and range of each function, we need to consider the x-values (years) and the y-values (population count) in the given data. In this case, the domain would be the set of years for which we have data, i.e., 1960, 1970, 1980, and 1990. The range would be the set of corresponding population counts, i.e., 181, 205, 228, and 250.
Once we have the equation of the linear function, we can use it to estimate the population count for any given year within the domain.
In conclusion, the context behind how the functions are being used is to describe the population growth over the years mentioned in the data. The domain represents the years for which we have data, and the range represents the corresponding population counts. Charts or graphs can be helpful for visualizing the data points and understanding the trend. Once we find the equation of the linear function, we can use it to estimate population counts for other years within the given domain.