below shows the number, in millions, graduating from high school in the United States in the given year.† Year Number 1975 3.13 1980 3.04 1985 2.68 1990 2.57 1994 2.46 1999 2.76 2004 3.05 2009 3.32 (a) Make a plot of the data. (Let N be the number, in millions, graduating from high school and let t be the number of years since 1975.) Explain why a linear model is not appropriate. The graph does not lie close to ---Select--- a single line multiple lines , so a linear model is not appropriate. (b) Use regression to find a linear model for the years 1975 through 1990. (Round regression line parameters to three decimal places.) N(t) = (c) Use regression to find a linear model for the years 1994 through 2009. (Round regression line parameters to three decimal places.) N(t) =
below shows the number, in millions, graduating from high school in the United States in the given year.† Year Number 1975 3.13 1980 3.04 1985 2.68 1990 2.57 1994 2.46 1999 2.76 2004 3.05 2009 3.32 (a) Make a plot of the data. (Let N be the number, in millions, graduating from high school and let t be the number of years since 1975.) Explain why a linear model is not appropriate. The graph does not lie close to ---Select--- a single line multiple lines , so a linear model is not appropriate. (b) Use regression to find a linear model for the years 1975 through 1990. (Round regression line parameters to three decimal places.) N(t) = (c) Use regression to find a linear model for the years 1994 through 2009. (Round regression line parameters to three decimal places.) N(t) =
Chapter5: Exponential And Logarithmic Functions
Section5.5: Exponential And Logarithmic Models
Problem 4ECP
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e below shows the number, in millions, graduating from high school in the United States in the given year.†
| Year | Number |
|---|---|
| 1975 | 3.13 |
| 1980 | 3.04 |
| 1985 | 2.68 |
| 1990 | 2.57 |
| 1994 | 2.46 |
| 1999 | 2.76 |
| 2004 | 3.05 |
| 2009 | 3.32 |
(a) Make a plot of the data. (Let N be the number, in millions, graduating from high school and let t be the number of years since 1975.)
Explain why a linear model is not appropriate.
(b) Use regression to find a linear model for the years 1975 through 1990. (Round regression line parameters to three decimal places.)
(c) Use regression to find a linear model for the years 1994 through 2009. (Round regression line parameters to three decimal places.)
(d) Write a formula for a model of the number, in millions, graduating as a piecewise-defined function using the linear models from part (b) and part (c).
(e) Make a graph of the formula you found in part (d).
(f) The number graduating in 1995 was 2.52 million. On the basis of your graph in part (e), determine how this compares with what would be expected from your formula.
Explain why a linear model is not appropriate.
The graph does not lie close to ---Select--- a single line multiple lines , so a linear model is not appropriate.
(b) Use regression to find a linear model for the years 1975 through 1990. (Round regression line parameters to three decimal places.)
N(t) =
(c) Use regression to find a linear model for the years 1994 through 2009. (Round regression line parameters to three decimal places.)
N(t) =
(d) Write a formula for a model of the number, in millions, graduating as a piecewise-defined function using the linear models from part (b) and part (c).
N =
|
|
for 0 ≤ t ≤ 15 | |
|
|
for 19 ≤ t ≤ 34 |
(e) Make a graph of the formula you found in part (d).
(f) The number graduating in 1995 was 2.52 million. On the basis of your graph in part (e), determine how this compares with what would be expected from your formula.
Using this formula to calculate N for 1995,
N
= 2.516 million.
Therefore, the actual number of 2.52 million is a little ---Select--- more less than would be expected from the formula.Expert Solution
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