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Discrete Functions Unit Assignment
You may choose to complete your mathematical calculations by hand and scan or
take images to upload to the dropbox. To help your teacher review your work,
submit your calculations as a single file document (preferably as a pdf). If you
aren’t sure how to do this, e-mail your teacher for assistance.
Important
When answering questions in a mathematics course always be sure to use
the following guidelines to help you do your best:
Provide full solution, showing all of your steps.
Make sure that there is one step or idea per line.
Use one equal sign per line.
Make sure that equal signs line up vertically.
Don’t use self-developed short form notations.
1. A high performance all-terrain vehicle (ATV) is bought at a price of $20,000. It
loses 10% of its value every year. Express this scenario as a sequence
recursively and explicitly (provide its general term). (3 marks)
2. Following one side of a new street in a neighbourhood, the house numbers
increase by six. The house number of the first house on the street is 319.
Express this sequence recursively and explicitly. (3 marks)
3. $100 is deposited at the end of every week for five years in an account that
pays 14%/a, compounded weekly. (2 marks each)
a. What type of annuity is this
Listen 21.11.2023 13:17 Di screte Functi ons Uni t Assi gnment
https://lms.vi rtualhi ghschool.com/d2l/le/enhancedSequenceVi ewer/64443 url=https%3A%2F%2F7373ee8e-81ee-4ff2-abda-d6a83ec1978f.sequ… 2/3
b. Find the future value of the annuity using the formula.
c. Find the future value of the annuity using a spreadsheet. In your answer
include the formulas that you typed.
d. Find the future value of the annuity using the TVM solver on a graphing
calculator or on a website. In your answer, include what values you typed
for each parameter.
4. Vanna has just financed the purchase of a home for $200,000. She agreed to
repay the loan by making equal monthly blended payments of $3,000 each at
4%/a, compounded monthly. (2 marks each)
a. Create an amortization table using a Microsoft Excel spreadsheet. In your
answer include all the formulas used.
b. How long will it take to repay the loan
c. How much will be the final payment
d. Determine how much interest she will pay for her loan.
e. Use Microsoft Excel to graph the amortization of the loan Hint
f. How much sooner would the loan be paid if she made a 15% down
payment
g. How much would Vanna have saved if she had obtained a loan 3%/a,
compounded monthly
h. Write a concluding statement about the importance of interest rates and
down payments when taking out loans.
5. A lottery offers two options for a prize, A and B, as shown below.
a. Which option would the winner choose if you expect to live for another: (2
marks)
20 years
50 years
b. Use technology to determine the range of life expectancies when each
option is preferred. Show your work. (2 marks)
c. Write a brief reflection about which option you would choose, and why. (3
marks)
Option A: $1,000 a week for life.
Option B: $1,000,000 in one lump sum.21.11.2023 13:17 Di screte Functi ons Uni t Assi gnment
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If you choose Option B, you have the opportunity to
place the winnings into an investment that also makes
regular payments, at a rate of 3%/a, compounded
weekly. The annuity will pay out a specific amount
weekly based on how long you want the annuity to
last.
6. Mary would like to save $10,000 at the end of 5 years for a future down
payment on a car. (3 marks each)
a. How much should she deposit at the end of each month in a savings
account that pays 1.2%/a, compounded monthly, to meet her goal
b. If you currently have a part-time job, consider your hourly wage. If you do
not have a job, use the minimum hourly wage in your jurisdiction. How
many hours each month would you have to work, just to make those
payments Write a brief reflection on the advantages and disadvantages to
long-term saving for a purchase, compared to borrowing a large sum of
money and paying it off over time. Note that interest rates for savings
accounts are always lower than interest rates for borrowing.
Submit this assignment to the dropbox. This assignment will be evaluated for a grade that will
contribute to your overall final grade in this course.23.11.2023 14:16 Explori ng Functi ons Uni t Assi gnment
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Exploring Functions Unit
Assignment
Congratulations! You’ve reached the first assignment in your course. To submit
your assignment, just navigate to the next page, upload your file(s), and select
the “Submit” button to submit the activity to your teacher. Before completing an
assignment, we recommend that you complete all of the practice activities in the
unit and wait for feedback. The feedback from the practice activities will help you
improve your understanding and will help you to achieve the best possible mark
on your assignments.
You may choose to complete your mathematical calculations by hand and scan or
take images to upload to the dropbox. To help your teacher review your work,
submit your calculations as a single file document (preferably as a pdf). If you
aren’t sure how to do this, please e-mail your teacher for assistance.
Important
When answering questions in a mathematics course always use the
following guidelines to help you do your best:
Provide full solutions, showing all of your steps.
Make sure that there is one step or idea per line.
Use one equal sign per line.
Make sure that equal signs line up vertically.
Don’t use self-developed short form notations.
Make sure all graphs are titled with labeled axes.
Listen 23.11.2023 14:16 Explori ng Functi ons Uni t Assi gnment
https://lms.vi rtualhi ghschool.com/d2l/le/enhancedSequenceVi ewer/64443 url=https%3A%2F%2F7373ee8e-81ee-4ff2-abda-d6a83ec1978f.sequ… 2/3
1. Answer the following for each of the given
relations. (4 marks each)
a. :See image
b.
c.
d.
Determine the domain and range using set
notation.
