The logistic model P(t) = OA. ⒸU. FU/ i5 te pervemage vi fiusenvius without a personal computer in 1990. III (b) Use a graphing utility to graph P = P(t). Choose the correct graph below. foll A 100 70 Years since 1986 95.4762 1+0.0352 0.1774t represents the percentage of households that do not own a personal computer t years since 1986. Complete parts (a) (d). Q usah OB. B. % Households 100- 0- 70 Years since 1988 Q Q 10003 OC. Households 100- 0- 70 Years since 1988 Q Households 100+ 70 Years since 1988 Q

Calculus: Early Transcendentals
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Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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To the expert who said it is not a complete question every part from A through C is there I need help with part C . The question is complete. This is Apart of a homework question. 

**Logistic Model Analysis for Household Computer Ownership**

The logistic model \( P(t) = \frac{95.4762}{1 + 0.0352 e^{0.1774t}} \) represents the percentage of households that do not own a personal computer \( t \) years since 1986. 

### Tasks and Solutions

**(b) Graphing the Model P(t):**

A graph utility is used to display \( P = P(t) \). The correct graph can be identified from the options provided.

- **Graph D:** This graph is characterized by a rapid decline from near 100% in 1986, showing a decrease in the percentage of households without a personal computer over time. The x-axis represents "Years since 1986," ranging from 0 to 70 years. The y-axis indicates the "% Households," ranging from 0 to 100%.

**(c) Percentage Calculation for 1999:**

What percentage of households did not own a personal computer in 1999?

- To find this percentage, substitute \( t = 13 \) (since 1999 is 13 years after 1986) into the logistic model.
- Calculate \( P(13) \) using the given formula.
- The result provides the percentage of households without a personal computer in 1999, rounded to one decimal place.

**Graph Explanation:**

Each graph option (A, B, C, D) depicts the relationship between the years since 1986 and the percentage of households without a personal computer. 

- **Graph A:** Shows an increase, which is not correct for this context.
- **Graph B:** Shows a more stable percentage, also incorrect.
- **Graph C:** Indicates an initial steep drop followed by stability, partially correct but not reflective over the full range.
- **Graph D:** Correctly shows a significant decrease, aligning with expected trends of increasing computer ownership over time.

This analysis helps illustrate the changes in computer ownership in households over time, offering insights into technological adoption trends.
Transcribed Image Text:**Logistic Model Analysis for Household Computer Ownership** The logistic model \( P(t) = \frac{95.4762}{1 + 0.0352 e^{0.1774t}} \) represents the percentage of households that do not own a personal computer \( t \) years since 1986. ### Tasks and Solutions **(b) Graphing the Model P(t):** A graph utility is used to display \( P = P(t) \). The correct graph can be identified from the options provided. - **Graph D:** This graph is characterized by a rapid decline from near 100% in 1986, showing a decrease in the percentage of households without a personal computer over time. The x-axis represents "Years since 1986," ranging from 0 to 70 years. The y-axis indicates the "% Households," ranging from 0 to 100%. **(c) Percentage Calculation for 1999:** What percentage of households did not own a personal computer in 1999? - To find this percentage, substitute \( t = 13 \) (since 1999 is 13 years after 1986) into the logistic model. - Calculate \( P(13) \) using the given formula. - The result provides the percentage of households without a personal computer in 1999, rounded to one decimal place. **Graph Explanation:** Each graph option (A, B, C, D) depicts the relationship between the years since 1986 and the percentage of households without a personal computer. - **Graph A:** Shows an increase, which is not correct for this context. - **Graph B:** Shows a more stable percentage, also incorrect. - **Graph C:** Indicates an initial steep drop followed by stability, partially correct but not reflective over the full range. - **Graph D:** Correctly shows a significant decrease, aligning with expected trends of increasing computer ownership over time. This analysis helps illustrate the changes in computer ownership in households over time, offering insights into technological adoption trends.
The logistic model \( P(t) = \frac{95.4762}{1 + 0.0352e^{0.1774t}} \) represents the percentage of households that do not own a personal computer \( t \) years since 1986. Complete parts (a)–(d).

---

(a) Evaluate and interpret \( P(0) \). Evaluate \( P(0) \).

\[ P(0) = 92.2\% \]

(Round to one decimal place as needed.)

Which sentence below best describes \( P(0) \)?

- A. \( P(0) \) is the year no households had a personal computer.
- B. \( P(0) \) is the year all households had a personal computer.
- C. \( P(0) \) is the percentage of households with a personal computer in 1986.
- D. \( P(0) \) is the percentage of households without a personal computer in 1986.

Selected Answer: 

- \( \checkmark \) D. \( P(0) \) is the percentage of households without a personal computer in 1986.
Transcribed Image Text:The logistic model \( P(t) = \frac{95.4762}{1 + 0.0352e^{0.1774t}} \) represents the percentage of households that do not own a personal computer \( t \) years since 1986. Complete parts (a)–(d). --- (a) Evaluate and interpret \( P(0) \). Evaluate \( P(0) \). \[ P(0) = 92.2\% \] (Round to one decimal place as needed.) Which sentence below best describes \( P(0) \)? - A. \( P(0) \) is the year no households had a personal computer. - B. \( P(0) \) is the year all households had a personal computer. - C. \( P(0) \) is the percentage of households with a personal computer in 1986. - D. \( P(0) \) is the percentage of households without a personal computer in 1986. Selected Answer: - \( \checkmark \) D. \( P(0) \) is the percentage of households without a personal computer in 1986.
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