Should be done in TI-nspire,
Assignment 2 Using CAS
BLACK CROW MALLEMUK
The relationship between the weight of a bird's egg and the thickness of the eggshell can be described by the model
Y = 0.0513*x0.456
where y is the thickness of the eggshell, measured in mm, and x is the weight of the egg, measured in grams.
a) How thick is the shell of an egg weighing 150 grams?
b) Solve the equation
0.0513* x0.456 = 0.3
and explain what the solution tells about bird eggs.
Eggs from a mallet weigh 5 times as much as eggs from a black crow.
A nature guide says that the shell on the mallemuk's egg is twice as thick as the shell on it
the black crow's eggs.
Exercise 3. Using CAS
China has experienced great economic growth for a number of years. Developments in China's gross domestic product
(GDP) for a period before the financial crisis can be approximately described by the model
F(x)=726 * 1.115x
where x is the number of years after 1995, and f(x) is China's GDP, measured in billions of dollars.
a) Determine China's GDP in the year 2001 according to the model.
b) What do the constants 726 and 1.115 tell us about China's GDP?
c) In what year will China's GDP reach $1200 billion according to the model?
d) Determine the doubling constant.
Explain what this figure tells about the development of China's GDP.
Assignment 4 – Using CAS
A Cooper test is a simple way to find a person's health status. The test is to run as long
a distance as possible in 12 minutes.
The following model can be used to a good approximation to describe the relationship between fitness numbers
and running distance (of 12 min) for men:
K(x) = 0.022x − 10.6
where K(x) is the fitness number and x is the distance the man can run (measured in meters).
A man completes a Cooper test and the fitness number is found to be 55.
a) Determine the distance the man could run in the test.
After a few months of training, he completes the test again. He can now run 450 meters further
than in the first test.
b) How much has his health score increased?
c) What does the number 0.022 tell us about men's fitness index?
Exercise 5. Using CAS.
The weight of a tropical conifer can be described by the model
f(d) = 0.31 * d2.11
where d is the diameter in cm at the base of the tree, and f(d) is the weight of the tree in kg.
a) What is the weight of a tropical conifer with a diameter of 15 cm?
b) What is the diameter of a tropical conifer weighing 150 kg?
c) If one tropical conifer has twice the diameter of another, how many times its
weight so greater?
Exercise 6A Using CAS
Argument for connection between a and b and the graph of linear functions
The price of driving a trip in a car purchased through a specific car sharing company can be calculated with it
linear calculation formula
f(x) = 1.5x + 48
where f(x) is the price in DKK, and x is the number of kilometers driven.
a) Use the calculation formula to fill in the blanks in the table below. Yours
intermediate bills must be included in the answer.
You can write the table with a math template (in TI-Nspire), see the image on the below.
b) Use the completed table to answer the following questions:
What happens to the value of f(x) when x is increased by 1?
c) Use the completed table to answer the following questions:
Where does the graph of the function intersect the y-axis?
Note: Your answers to the previous two questions should be consistent with what you already know the meaning of the constants a and b in linear functions.
Argument for connection between a and b and the graph of exponential functions.
The rest of Exercise 6A is about the exponential function with the formula:
g(x) = 3 · 2x
d) Use the formula to fill in the blanks in the table below. The intermediate bills
must be included in the answer.
Help for the task: Remember that 20 = 1, since any number other than 0 raised to 0 gives 1.
e) Use the completed table to answer the following questions:
What happens to the value of g(x) when x is increased by 1?
f) Use the completed table to answer the following questions:
Where does the graph of the function intersect the y-axis?
Evaluation sheet
After you have calculated the tasks, you must check the result and production with this evaluation sheet.
Task 1
Did you remember to write the focal point you were given by your teacher into your assignment?
Are you aware that this is something you must focus on in all future answers?
If you have been given a focus task, you must answer it as Task 1.
Assignment 2
a) Consider whether 150 is an x-value or a y-value. Have you found the answer 0.5 mm?
b) Consider whether the number 0.3 is an x-value or a y-value. The solution to the equation is 48.1. Do you have
remembered to formulate a general sentence about what this number tells about the context
between the weight of a bird's egg and the thickness of the shell?
Task 4
a) Have you considered whether it is a �-value or a �-value you are being informed about? Result 2982 m
b) Have you noticed that it says that the man can run 450 m further? The number of sweets has also increased
9.9.
c) Consider what the slope coefficient means in a linear function.
Module 5B – Online mathematics C Page 8 of 9
Task 5
a)+b) Tip: A common mistake in this type of task is to swap "x" and "y". Read carefully
the task text: do you know d or f(d)?
c) Hint: You can use the formula Fy = (Fx )a. When something "is twice as big" it belongs
projection factor 2
Exercise 6A
Have you arrived at the values below? Did you remember to show your calculation ?
b) Does your answer agree with what you already knew about the meaning of the constant a in a
linear function?
c) Have you explained how the intersection of the graph with the y-axis appears from the table? Voices yours answer consistent with what you already knew about the meaning of the constant b in a linear function?
d) Have you arrived at the values below? Did you remember to show your calculations
e) Does your answer agree with what you already knew about the meaning of the constant a in a
exponential function?
f) Have you explained how the intersection of the graph with the y-axis appears from the table? Voices yours
answer consistent with what you already knew about the meaning of the constant b in an exponential
function
