Concept explainers
U.S. Population The U.S. Constitution requires a census every 10 years. The census data for 1790–2010 are given in the table.
(a) Make a
(b) Use a calculator to find an exponential model for the data.
(c) Use your model to predict the population at the 2020 census.
(d) Use your model to estimate the population in 1965.
Year | Population (in millions) | Year | Population (in millions) | Year | Population (in millions) |
1790 1800 1810 1820 1830 1840 1850 1860 |
3.9 5.3 7.2 9.6 12.9 17.1 23.2 31.4 |
1870 1880 1890 1900 1910 1920 1930 1940 |
38.6 50.2 63.0 76.2 92.2 106.0 123.2 132.2 |
1950 1960 1970 1980 1990 2000 2010 |
151.3 179.3 203.3 226.5 248.7 281.4 308.7 |
a)
To make:
A scatter plot for the given data.
Year | Population (in millions) |
1790 | 3.9 |
1800 | 5.3 |
1810 | 7.2 |
1820 | 9.6 |
1830 | 12.9 |
1840 | 17.1 |
1850 | 23.2 |
1860 | 31.4 |
1870 | 38.6 |
1880 | 50.2 |
1890 | 63.0 |
1900 | 76.2 |
1910 | 92.2 |
1920 | 106.0 |
1930 | 123.2 |
1940 | 132.2 |
1950 | 151.3 |
1960 | 179.3 |
1970 | 203.3 |
1980 | 226.5 |
1990 | 248.7 |
2000 | 281.4 |
2010 | 308.7 |
Explanation of Solution
By plotting the data points in the table, we get the scatter plot as follows.
Therefore, the scatter plot for the given data constructed.
b)
To find:
An exponential model for the given data using calculator.
Answer to Problem 1P
Solution:
The exponential model for the given data using a calculator is
Explanation of Solution
Using a graphing calculator and the Exp Reg command, we get the exponential model
In the above equation P-represents the population (in million) and t-represents the year. Since 1790.
Therefore, the exponential model for the given data using a calculator is
c)
To find:
The population at the 2020 census.
Answer to Problem 1P
Solution:
The population at the 2020 census
Explanation of Solution
The exponential model of the data is given by
Take,
Therefore, the population at the 2020 census
d)
To find:
The population at the 1965 census.
Answer to Problem 1P
Solution:
The pollution at the 1965 census is
Explanation of Solution
The exponential model of the data is given by
Therefore, the pollution at the 1965 census is
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