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
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter9: Quadratic Functions And Equations
Section9.2: Transformations Of Quadratic Functions
Problem 49PFA
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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
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