11. The Australian Teal Frog is a species that has become endangered due to inability to defend itself against birds such as crows, eagles, and swans. In order to try and save the frogs, a colony was established on Fantasy Island. The number F(t) of frogs after t months can be modelled by the function: F(t) = t³ - 21t² + 120t + 12 The graph of F(t) against t is shown below. >> F(t) 3004 200 150 100 10 d Marko 11 a. Write down F'(t) b. Find the values of F (2) and F'(2) c. Interpret your answers to part (b) in the context of the population of the Australian Teal Frog * I+Y (1) pwd by desmos
11. The Australian Teal Frog is a species that has become endangered due to inability to defend itself against birds such as crows, eagles, and swans. In order to try and save the frogs, a colony was established on Fantasy Island. The number F(t) of frogs after t months can be modelled by the function: F(t) = t³ - 21t² + 120t + 12 The graph of F(t) against t is shown below. >> F(t) 3004 200 150 100 10 d Marko 11 a. Write down F'(t) b. Find the values of F (2) and F'(2) c. Interpret your answers to part (b) in the context of the population of the Australian Teal Frog * I+Y (1) pwd by desmos
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section: Chapter Questions
Problem 30P: In this problem you are asked to find a function that models in real life situation and then use the...
Related questions
Question
100%
I know it’s a long question but if you could show me all parts would be highly appreciated it would help me for my test thanks
![11. The Australian Teal Frog is a species that has become endangered due to inability to defend itself
against birds such as crows, eagles, and swans. In order to try and save the frogs, a colony was
established on Fantasy Island.
The number F(t) of frogs after t months can be modelled by the function:
F(t) = t³ 21t² + 120t + 12
The graph of F(t) against t is shown below.
>> F(1)
300A
250
200
150
100
10
11
(0)
a. Write down F' (t)
b. Find the values of F (2) and F'(2)
c. Interpret your answers to part (b) in the context of the population of the Australian Teal
Frog
d. Mark on the diagram the approximate position of any horizontal tangents to the curvel
e. Use algebra to find the t coordinate of these points
f.
Hence state the time period over which the frog population was decreasing and determine
the total decline in the number of frogs during this time.
* I+Y
powered by
desmos](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7a1d7933-34c3-4041-8ba5-cd9ccd276518%2F7def30d5-6e46-474e-972a-f30b6f5055d4%2F6ghilq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:11. The Australian Teal Frog is a species that has become endangered due to inability to defend itself
against birds such as crows, eagles, and swans. In order to try and save the frogs, a colony was
established on Fantasy Island.
The number F(t) of frogs after t months can be modelled by the function:
F(t) = t³ 21t² + 120t + 12
The graph of F(t) against t is shown below.
>> F(1)
300A
250
200
150
100
10
11
(0)
a. Write down F' (t)
b. Find the values of F (2) and F'(2)
c. Interpret your answers to part (b) in the context of the population of the Australian Teal
Frog
d. Mark on the diagram the approximate position of any horizontal tangents to the curvel
e. Use algebra to find the t coordinate of these points
f.
Hence state the time period over which the frog population was decreasing and determine
the total decline in the number of frogs during this time.
* I+Y
powered by
desmos
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
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 2 steps with 1 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![College Algebra](https://www.bartleby.com/isbn_cover_images/9781305115545/9781305115545_smallCoverImage.gif)
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
![College Algebra (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305652231/9781305652231_smallCoverImage.gif)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![College Algebra](https://www.bartleby.com/isbn_cover_images/9781305115545/9781305115545_smallCoverImage.gif)
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
![College Algebra (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305652231/9781305652231_smallCoverImage.gif)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![Algebra for College Students](https://www.bartleby.com/isbn_cover_images/9781285195780/9781285195780_smallCoverImage.gif)
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
![Glencoe Algebra 1, Student Edition, 9780079039897…](https://www.bartleby.com/isbn_cover_images/9780079039897/9780079039897_smallCoverImage.jpg)
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
![Intermediate Algebra](https://www.bartleby.com/isbn_cover_images/9780998625720/9780998625720_smallCoverImage.gif)