## Rosette & Frieze Patterns

## Rule of 70 & Real GDP

As we discussed in class, the Rule of 70 is used to figure out how quickly something will double when it is growing exponentially. When you divide 70 by the percent increase the outcome is the doubling time. When you divide 70 by the doubling time the outcome is the growth. The Rule of 70 is often used to predict population growth but it has other uses as well. One of these other useful applications of the rule is estimating how long it would take a country’s real gross domestic product to double. Here you use the GDP growth rate in the divisor of the rule which is similar to calculating compound interest rates.

For example, if the growth rate of Japan is 10%, the Rule of 70 predicts that it would take seven years for Japan’s real GDP to double.

That being said, it is important to remember that the Rule of 70 is only an estimate based on forecasted growth rates. Therefore, if the rate of growth fluctuate then the original calculation may be inaccurate. Because of this, the Rule of 70 should not be used where growth rates are anticipated to vary dramatically.

## Do Elections Work? Voting Thoery

There has been a lot of controversy over whether or not the methods used to count votes in elections is effective or fair. An example of this controversy is from December of 2017 when the mayor of San Francisco, Ed Lee, passed away and had to be replaced. San Francisco uses whats called ranked choice voting, or the instant runoff method. The voters rank three choices in order of their preference and then when the votes are counted, the choice who got the least first place votes gets dropped and their points go to the voters’ second choices. Even though many people think this method of counting votes is unfair, it is actually one of the most accurate methods. The counting method of plurality makes sense but doesn’t work well when there are more than two voting choices.

The other problem with the plurality method of counting votes is that it violates Condorcet’s Theory which says that an election should be won by a candidate who would beat all the other candidates head-to-head.

## Proportional Tax!

In New Hampshire we have a progressive tax system where the tax rates are adjusted by the income individuals make. As we talked about in class, a progressive tax system benefits those who have a lower income and may not benefit those with a higher income because they are required to pay a higher tax rate. After learning about progressive and regressive tax systems in class, I thought it would be interesting to find out more about proportional tax which is an income tax system where the same percentage of tax is applied to all taxpayers no matter how much their income is. It is interesting to note that sales tax is also considered a type of proportional tax because all customers are paying the same rate on goods and services. Luckily, New Hampshire does not have a sales tax but we pay for this in other ways such as having high property taxes.

An example of proportional tax is when the rate is set at 20%. Someone earning $10,000 would pay $2,000 in taxes, someone earning $50,000 would pay $10,000, and someone earning $100,000,000 would pay $200,000 in taxes. I believe a proportional tax system is more fair than a regressive or progressive tax system because everyone is being taxed equally according to their income.

Of course there are still pros and cons of a proportional tax system. Technically, it is considered a regressive tax system because the rates don’t increase as the income amounts increase. Also, people who are against proportional tax feel as if those who have a higher income should be paying a higher tax rate than the lower class.

Below is a figure which compares regressive, progressive, and proportional taxes.

## Blog Test

Hey everyone! I am not a huge fan of math but I am excited for this course because it looks as if we will be learning information that can be applied to everyday life.