8. The percent p a stock price has fluctuated in one year can be modeled by p(x) = 0.0005x¹-0.0193x³ +0.243x² - 1.014x + 1.04, where x is the number of months since January. a. Use a graphing calculator to graph the function. b. State the relevant domain and estimate the range c. Use the graph to approximate the y-intercept. Then find the y- intercept algebraically. What does the y-intercept represent? d. Find and interpret any zeros of the function.
8. The percent p a stock price has fluctuated in one year can be modeled by p(x) = 0.0005x¹-0.0193x³ +0.243x² - 1.014x + 1.04, where x is the number of months since January. a. Use a graphing calculator to graph the function. b. State the relevant domain and estimate the range c. Use the graph to approximate the y-intercept. Then find the y- intercept algebraically. What does the y-intercept represent? d. Find and interpret any zeros of the function.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![**Problem Statement:**
The percentage \( p \) a stock price has fluctuated in one year can be modeled by the function:
\[ p(x) = 0.0005x^4 - 0.0193x^3 + 0.243x^2 - 1.014x + 1.04 \]
where \( x \) is the number of months since January.
**Tasks:**
a. **Graph the Function**
- Use a graphing calculator to plot the function \( p(x) \).
b. **Domain and Range**
- State the relevant domain and estimate the range of the function.
c. **Y-Intercept**
- Use the graph to approximate the y-intercept. Then find the y-intercept algebraically.
- Explain what the y-intercept represents in this context.
d. **Zeros of the Function**
- Find and interpret any zeros of the function. Explain their significance in terms of stock price fluctuation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5be08870-42d5-4312-a3e5-4e13c9d78dbe%2F25d92306-3015-4287-9abf-60368da5c5b7%2Fhzs541p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
The percentage \( p \) a stock price has fluctuated in one year can be modeled by the function:
\[ p(x) = 0.0005x^4 - 0.0193x^3 + 0.243x^2 - 1.014x + 1.04 \]
where \( x \) is the number of months since January.
**Tasks:**
a. **Graph the Function**
- Use a graphing calculator to plot the function \( p(x) \).
b. **Domain and Range**
- State the relevant domain and estimate the range of the function.
c. **Y-Intercept**
- Use the graph to approximate the y-intercept. Then find the y-intercept algebraically.
- Explain what the y-intercept represents in this context.
d. **Zeros of the Function**
- Find and interpret any zeros of the function. Explain their significance in terms of stock price fluctuation.
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