Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Chapter 1 homework
**Educational Content: Population Modeling Exercise**

**Description:**

The bar graph shows the population of a country, in millions, for seven selected years. The two functions that are given model the data: the male population, \( M(x) \), in millions, and the female population, \( F(x) \), in millions, x years after 1985. Answer parts a through c.

\[ M(x) = 1.47x + 118.5 \]
\[ F(x) = 1.45x + 120.5 \]

**Part a.** Write a function that models the total population of a country for the years shown in the bar graph. Select the correct choice below and fill in the answer box to complete your choice.

- A. \((M + F)(x) = \_\_\_\)
- B. \((MF)(x) = \_\_\_\)
- C. \((M - F)(x) = \_\_\_\)
- D. \( \left( \frac{M}{F} \right) (x) = \_\_\_\)

**Part b.** Use the function from part (a) to find the total population of a country in 2010.

The total population of a country in 2010 is \_\_\_ million. (Type an integer or a decimal.)

**Part c.** How well does the result in part (b) model the actual total population in 2010 shown by the bar graph? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Type an integer or a decimal.)

- A. The result in part (b) underestimates the actual population of a country in 2010 by \_\_\_ million.
- B. The result in part (b) overestimates the actual population of a country in 2010 by \_\_\_ million.
- C. The result in part (b) and the actual number of total population of a country in 2010 is the same.

**Graph Description:**

The graph titled "Population of the Country" displays the population figures in millions on the Y-axis and the years 1985, 1990, 1995, 2000, 2005, 2010, and 2015 on the X-axis. Each year has two bars: one representing the male population (in
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Transcribed Image Text:**Educational Content: Population Modeling Exercise** **Description:** The bar graph shows the population of a country, in millions, for seven selected years. The two functions that are given model the data: the male population, \( M(x) \), in millions, and the female population, \( F(x) \), in millions, x years after 1985. Answer parts a through c. \[ M(x) = 1.47x + 118.5 \] \[ F(x) = 1.45x + 120.5 \] **Part a.** Write a function that models the total population of a country for the years shown in the bar graph. Select the correct choice below and fill in the answer box to complete your choice. - A. \((M + F)(x) = \_\_\_\) - B. \((MF)(x) = \_\_\_\) - C. \((M - F)(x) = \_\_\_\) - D. \( \left( \frac{M}{F} \right) (x) = \_\_\_\) **Part b.** Use the function from part (a) to find the total population of a country in 2010. The total population of a country in 2010 is \_\_\_ million. (Type an integer or a decimal.) **Part c.** How well does the result in part (b) model the actual total population in 2010 shown by the bar graph? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Type an integer or a decimal.) - A. The result in part (b) underestimates the actual population of a country in 2010 by \_\_\_ million. - B. The result in part (b) overestimates the actual population of a country in 2010 by \_\_\_ million. - C. The result in part (b) and the actual number of total population of a country in 2010 is the same. **Graph Description:** The graph titled "Population of the Country" displays the population figures in millions on the Y-axis and the years 1985, 1990, 1995, 2000, 2005, 2010, and 2015 on the X-axis. Each year has two bars: one representing the male population (in
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