Description
Solve the inequality symbolically. Express the solution set in interval notation.
1-x/4 < 2x-2/7
A screenshot of this problem is provided for clarification. Answer the other questions posted below.
Some discussion points you can address this week:
1. In finance, simple interest is a linear growth of interest over time. How would you describe what simple interest is to a 5 year old?
2. Let's say you invested some money in an account and had an option to choose Linear Growth for your returns, or Exponential Growth instead. Which one might you choose and why?
3. What is the coolest looking inequality you can draw on Desmos? https://www.desmos.com/calculator
4. If you saw an ad that said: "you can save up to 50% on a new car!", what would that look like as an inequality? Do you think most people actually save 50%?
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Explanation & Answer
Hi! Attached is a word document containing all of the solutions to the questions - I hope you are happy with them (and hope you find the inequalities on Desmos amusing!).Of course, if there is anything you would like me to change/revisit, please just message me and I am more than happy to rework anything you ask me to!
Math answers
Inequality question
Image of working-out:
Therefore, x is in the range (1, ∞)
Discussion points
Question 1
When you give your money to a bank to look after for you, they give you a present as a ‘thank you’
for trusting them with your money. The present is even more money! We call this ‘interest’, and
usually it is paid either every month or every year. One version of this is called ‘simple interest’,
where the bank gives you a fixed amount of money every time they give you interest.
For example, if you leave $100 in a bank account, they might give you $10 a year just for lending
your money to them! So, after 2 years, you will have earned $20.
Question 2
Generally, I would pick exponential growth for my returns. This is because, with exponential growth,
the amount of money I earn in interest in each time interval is proportional to the money in my
account in that time interval, meaning that the interest will increase year-on-year as long as I keep
the money in the bank account. Over time, the amount of interest I earn will really start piling up.
For example, 1.0515=2.08 (2 decimal places): with an interest rate of 5% compound interest
(exp...