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User EdeDJ
31/08/2022
Maths
Recurrence Relations - word problems notes
Recurrence relations are a crucial topic in Higher Maths, often appearing in GCSE and A Level Maths exams. This guide explores word problems involving recurrence relations, providing examples of loan calculations and drug dosage scenarios. These problems are common in Higher Maths past papers and are essential for understanding sequences and financial mathematics.
31/08/2022
28
This page introduces a recurrence relation word problem focused on loan repayment calculations. It demonstrates how to use recurrence relations to model financial scenarios, a common topic in Higher Maths and A Level Maths.
The problem presents Betty's loan of £2000 with a 1.5% monthly interest rate and £450 monthly repayments. Students are tasked with creating a recurrence relation to model the loan balance over time.
Definition: A recurrence relation for this loan scenario is given as Bn+1 = 1.015Bn - 450, where Bn represents the balance after n months.
The page walks through the calculation process month by month, showing how the loan balance decreases over time. This step-by-step approach is valuable for students learning to apply recurrence relations to real-world problems.
Example: The calculation shows that by the end of May, the balance owed is £281.82058, and the final payment is made in June.
The problem also asks students to calculate the total amount Betty will have paid, which comes to £2086.05. This illustrates the concept of total interest paid on a loan, an important aspect of financial mathematics.
Highlight: For questions involving exceeding or dropping below specific limits, it's crucial to consider the values both before and after each payment or change.
This page effectively demonstrates the application of recurrence relations in financial contexts, providing a practical example that students might encounter in Higher Maths past papers or A Level Maths exams.
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Recurrence relations are a crucial topic in Higher Maths, often appearing in GCSE and A Level Mathsexams. This guide explores word problems involving recurrence relations, providing examples of loan calculations and drug dosage scenarios. These problems are common... Show more
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This page introduces a recurrence relation word problem focused on loan repayment calculations. It demonstrates how to use recurrence relations to model financial scenarios, a common topic in Higher Maths and A Level Maths.
The problem presents Betty's loan of £2000 with a 1.5% monthly interest rate and £450 monthly repayments. Students are tasked with creating a recurrence relation to model the loan balance over time.
Definition: A recurrence relation for this loan scenario is given as Bn+1 = 1.015Bn - 450, where Bn represents the balance after n months.
The page walks through the calculation process month by month, showing how the loan balance decreases over time. This step-by-step approach is valuable for students learning to apply recurrence relations to real-world problems.
Example: The calculation shows that by the end of May, the balance owed is £281.82058, and the final payment is made in June.
The problem also asks students to calculate the total amount Betty will have paid, which comes to £2086.05. This illustrates the concept of total interest paid on a loan, an important aspect of financial mathematics.
Highlight: For questions involving exceeding or dropping below specific limits, it's crucial to consider the values both before and after each payment or change.
This page effectively demonstrates the application of recurrence relations in financial contexts, providing a practical example that students might encounter in Higher Maths past papers or A Level Maths exams.
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Improve your grades
Join milions of students
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This document covers two main types of recurrence relation word problems: loan repayments and drug dosage calculations. These examples demonstrate the practical applications of recurrence relations in real-world scenarios.
The first problem involves a reducing balance loan scenario where Betty borrows £2000 with monthly repayments and interest.
Example: Betty takes out a £2000 loan with 1.5% monthly interest and £450 monthly repayments.
The recurrence relation for the loan balance is derived:
Definition: Bn+1 = 1.015Bn - 450, where Bn is the balance after n months.
The problem is solved step-by-step, showing how the loan balance decreases each month until the final payment in June.
Highlight: The final payment is made in June, with a total repayment of £2086.05.
The second problem involves calculating drug levels in a patient's bloodstream using recurrence relations.
Example: A drug with an initial dose of 120ml is administered, with 50% metabolized hourly and 35ml top-ups given each hour.
Two recurrence relations are presented:
Vocabulary: Metabolised - The process by which a drug is broken down in the body.
The problem is solved to determine when the drug level falls below the effective threshold of 58ml.
Highlight: The treatment stops being effective between the 3rd and 4th doses when the drug level drops below 58ml.
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The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
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This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
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Best app on earth! no words because it’s too good
Thomas R
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Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
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The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
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In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
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I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
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