00 nce observations of the island began. Graph the function P in an appropriate viewin- Im population attained? (Round your answer to one decimal place.) opulation? (Round your answer to the nearest whole number.) it population disappear from the island? (Round your answer to one decimal place.)
00 nce observations of the island began. Graph the function P in an appropriate viewin- Im population attained? (Round your answer to one decimal place.) opulation? (Round your answer to the nearest whole number.) it population disappear from the island? (Round your answer to one decimal place.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please answer as soon as you can thank you !
![The image presents the following text and graph as a mathematical problem related to population dynamics:
---
**Equation:**
\[ P(t) = 140t^2 - 0.4t^4 + 1300 \]
where \( t \) is the time (in months) since observations of the island began.
Graph the function \( P \) in an appropriate viewing rectangle, and use the graph to answer the following questions.
**Questions:**
(a) When is the maximum population attained? (Round your answer to one decimal place.)
(b) What is the maximum population? (Round your answer to the nearest whole number.)
(c) When does the rabbit population disappear from the island? (Round your answer to one decimal place.)
---
**Graph Description:**
The graph depicts a curve representing the function \( P(t) = 140t^2 - 0.4t^4 + 1300 \). The horizontal axis is labeled \( t \) (time in months), and the vertical axis is labeled \( P(t) \) (population). The curve starts at a high population level, rises to a peak point indicating maximum population, and then declines, eventually reaching the horizontal axis, suggesting the population decreases to zero.
The curve is crucial for visually identifying the answers to the questions posed, such as the time at which the population reaches its maximum and when it diminishes completely.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb96cbef8-ab64-43b1-a923-6a8582f58768%2F19b7abf7-9122-483f-81d7-9884f065ede4%2Fmufe9mg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image presents the following text and graph as a mathematical problem related to population dynamics:
---
**Equation:**
\[ P(t) = 140t^2 - 0.4t^4 + 1300 \]
where \( t \) is the time (in months) since observations of the island began.
Graph the function \( P \) in an appropriate viewing rectangle, and use the graph to answer the following questions.
**Questions:**
(a) When is the maximum population attained? (Round your answer to one decimal place.)
(b) What is the maximum population? (Round your answer to the nearest whole number.)
(c) When does the rabbit population disappear from the island? (Round your answer to one decimal place.)
---
**Graph Description:**
The graph depicts a curve representing the function \( P(t) = 140t^2 - 0.4t^4 + 1300 \). The horizontal axis is labeled \( t \) (time in months), and the vertical axis is labeled \( P(t) \) (population). The curve starts at a high population level, rises to a peak point indicating maximum population, and then declines, eventually reaching the horizontal axis, suggesting the population decreases to zero.
The curve is crucial for visually identifying the answers to the questions posed, such as the time at which the population reaches its maximum and when it diminishes completely.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 1 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
