The following table shows the number, in millions, graduating from high school in the United States in the given year. After 1992, the number of high school graduates has increased each year.| Year | Number graduating (in millions) ||------|---------------------------------|| 1985 | 2.83 || 1987 | 2.65 || 1989 | 2.47 || 1991 | 2.29 |(a) By calculating differences, show that these data can be modeled using a linear function. (Let $ d $ be years since 1985 and $ N $ the number of graduating high school students, in millions.)\[\begin{array}{|c|c|c|}\hline\text{ } & \text{1985 to 1987} & \text{1987 to 1989} & \text{1989 to 1991} \\\hline\text{Change in } d & 2 & 2 & 2 \\\hline\text{Change in } N & -0.18 & -0.18 & -0.18 \\\hline\end{array}\](b) What is the slope for the linear function modeling high school graduations? (Round your answer to two decimal places.)\[ -0.09 \text{ million per year} \]Explain in practical terms the meaning of the slope.This means that each year 0.09 million fewer high school students graduated.(c) Find a formula for a linear function that models these data. (Let $ d $ be years since 1985 and $ N $ the number of graduating high school students, in millions.)\[ N = \](d) Express, using functional notation, the number graduating from high school in 1994.\[ N( \]Calculate that value.\[ 2.02 \text{ million} \] This exercise represents a hypothetical implementation of the experiment suggested by Newton's second law of motion, which states that Force = Mass × Acceleration. A mass of 18 kilograms was subjected to varying accelerations, and the resulting force was measured. In the following table, acceleration is in meters per second per second, and force is in newtons.| Acceleration | Force ||--------------|-------|| 6 | 108 || 9 | 162 || 12 | 216 || 15 | 270 || 18 | 324 |### (a) Construct a table of differences.| Step | Change in A | Change in F ||-------|-------------|-------------|| Step 1| 3 | 54 || Step 2| 3 | 54 || Step 3| 3 | 54 || Step 4| 3 | 54 |**Explain how it shows that these data are linear.**For each change of 54 in F (Step 1 to Step 2) there is an increase of 3 in A.### (b) Find a linear model for the data. (Enter your answer in terms of A.)F = 3A### (c) Explain in practical terms what the slope of this linear model is.The slope is [Select] used in the experiment.### (d) Express using function notation, the force resulting from an acceleration of 14 meters per second per second.F(14) = NCalculate the force resulting from an acceleration of 14 meters per second per second.### (e) Explain how this experiment provides further evidence for Newton's second law of motion.F = [Select] × A, so Force = Mass × [Select].

a) From the table 1985-87 1987-89 1989-91 Change in d 1987-1985=2 1989-1987=2 1991-1989…

The following table shows the number, in millions, graduating from high school in the United States in the given year.t After 1992, the number of high school graduates has increased each year. Year Number graduating (in millions) 1985 2.83 1987 2.65 2.47 1989 1991 2.29 (a) By calculating differences, show that these data can be modeled using a linear function. (Let d be years since 1985 and N the number of graduating high school students, in millions.) 1985 to 1987 1987 to 1989 1989 to 1991 Change in d 2 2 Change in N -0.18 -0.18 -0.18 (b) What is the slope for the linear function modeling high school graduations? (Round your answer to two decimal places.) -0.09 million per year Explain in practical terms the meaning of the slope. This means that each year fewer v high school students graduated. (c) Find a formula for a linear function that models these data. (Let d be years since 1985 and N the number of graduating high school students, in millions.)

The following table shows the number, in millions, graduating from high school in the United States in the given year.t After 1992, the number of high school graduates has increased each year. Year Number graduating (in millions) 1985 2.83 1987 2.65 2.47 1989 1991 2.29 (a) By calculating differences, show that these data can be modeled using a linear function. (Let d be years since 1985 and N the number of graduating high school students, in millions.) 1985 to 1987 1987 to 1989 1989 to 1991 Change in d 2 2 Change in N -0.18 -0.18 -0.18 (b) What is the slope for the linear function modeling high school graduations? (Round your answer to two decimal places.) -0.09 million per year Explain in practical terms the meaning of the slope. This means that each year fewer v high school students graduated. (c) Find a formula for a linear function that models these data. (Let d be years since 1985 and N the number of graduating high school students, in millions.)

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

The following table shows the number, in millions, graduating from high school in the United States in the given year. After 1992, the number of high school graduates has increased each year.

| Year | Number graduating (in millions) |
|------|---------------------------------|
| 1985 | 2.83 |
| 1987 | 2.65 |
| 1989 | 2.47 |
| 1991 | 2.29 |

(a) By calculating differences, show that these data can be modeled using a linear function. (Let $ d $ be years since 1985 and $ N $ the number of graduating high school students, in millions.)

\[
\begin{array}{|c|c|c|}
\hline
\text{ } & \text{1985 to 1987} & \text{1987 to 1989} & \text{1989 to 1991} \\
\hline
\text{Change in } d & 2 & 2 & 2 \\
\hline
\text{Change in } N & -0.18 & -0.18 & -0.18 \\
\hline
\end{array}
\]

(b) What is the slope for the linear function modeling high school graduations? (Round your answer to two decimal places.)

\[ -0.09 \text{ million per year} \]

Explain in practical terms the meaning of the slope.

This means that each year 0.09 million fewer high school students graduated.

(c) Find a formula for a linear function that models these data. (Let $ d $ be years since 1985 and $ N $ the number of graduating high school students, in millions.)

\[ N = \]

(d) Express, using functional notation, the number graduating from high school in 1994.

\[ N( \]

Calculate that value.

\[ 2.02 \text{ million} \]

This exercise represents a hypothetical implementation of the experiment suggested by Newton's second law of motion, which states that Force = Mass × Acceleration. A mass of 18 kilograms was subjected to varying accelerations, and the resulting force was measured. In the following table, acceleration is in meters per second per second, and force is in newtons.

| Acceleration | Force |
|--------------|-------|
| 6 | 108 |
| 9 | 162 |
| 12 | 216 |
| 15 | 270 |
| 18 | 324 |

### (a) Construct a table of differences.

| Step | Change in A | Change in F |
|-------|-------------|-------------|
| Step 1| 3 | 54 |
| Step 2| 3 | 54 |
| Step 3| 3 | 54 |
| Step 4| 3 | 54 |

**Explain how it shows that these data are linear.**

For each change of 54 in F (Step 1 to Step 2) there is an increase of 3 in A.

### (b) Find a linear model for the data.

(Enter your answer in terms of A.)

F = 3A

### (c) Explain in practical terms what the slope of this linear model is.

The slope is [Select] used in the experiment.

### (d) Express using function notation, the force resulting from an acceleration of 14 meters per second per second.

F(14) = N

Calculate the force resulting from an acceleration of 14 meters per second per second.

### (e) Explain how this experiment provides further evidence for Newton's second law of motion.

F = [Select] × A, so Force = Mass × [Select].

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