## Tuesday, October 30, 2012

### Discussion question (for credit) plus entertainment from the choir drop outs

We I was in school all these years ago I was told be a teacher that the most important idea known to man was compounding interest (exponential growth).  What did they mean and what are the consequences to society and human kind of this mathematical relationship?

Think about this and then respond to this posting.  Here is some music for you to ponder first.
Choir Drop Outs Seek Revenge

1. Your teacher meant that compounding interest was so important because a number can start very small and if it grows exponentially, it gets to be a huge number very quickly. An example of how this effects society and mankind is that if an ant colony starts in Slavens with 4 ants that get in the building and the population grows by 4 times every week, then in 15 weeks there will be over 32,000 ants. If there were 32,00 ants in the school in just 4 months, then the school would be gross with so many ants. This exponential relationship works with other things like money, too. It is a very powerful relationship in the world.

2. Your teacher was talking about stock and how important it is to invest. If you invest a small amount of money it can exponentially grow each year into a larger amount of money. The consequence between someone who does invest money and someone who does is that the person who does invest money will have more money in the long run than the person who didn't invest.

3. Your teacher ment that compounding interest, exponential growth is very important because it can grow things very quickly. Money is a great example of this because. If you invest money then each year it will grow in amount because of exponential growth. If you were to invest \$10,000 and it had a 4% growth rate then each year you would increase your money by a growth factor of 1.04. This would menan that by the third year you would already have \$11,248.64. This means in three years you earned \$1,248.64 by doing nothing. This has consequences to society because everyday people deal with exponential growth. This has consequences to human kind by humans having to deal with exponential growth every day. We even learned that the CO2 level for pollution is growing each year exponentially.

4. Your teacher was trying to explain that exponential growth is very important in many things such as stocks and especially when it comes to investing in stocks. If you were to invest \$2000 every year starting at the age 18 and continually investing until you were 48 and the growth rate was 5% then in the end you could make a comfortable living settlement for yourself for a couple of years. However, if you choose to ignore the equation [y=a(b)^x], then you would have to suffer the consequence of not having as much money as you could with the investment.

5. Your teacher was explaining how exponential equations fit into everyday life. For instance if you're trying to find the population of an area over a few years and the population is growing exponentially. You would use y=a(b)^x which is the equation for an exponential growth. For example, if I want to find how much money I have if I invest \$5,000 into an investment with a 5% growth rate over 5 years. I just need to plug these numbers into the equation. So y=5000(1.05)^5 and that's how you find the answer. As you can see exponential growths can greatly impact everyday life.

6. Your teacher meant that exponential growth was the most important growth to understand because it is used most often in our society. One example that affects our society through exponential decay is bacteria. There are currently 80,000 bacteria in our culture and when an antibiotic is added, the population reduces by half every 3 hours. That means the decay factor would be 1/2 or .5% Other situations with exponential decay and growth that affect us are more studies of populations, electricity, temperatures, credit card payments, and many more things that model the relationship. Your teacher was obviously correct when she said that about exponential equations.

1. Your teacher meant that expotential growth is important for society and is important when investing in stocks. An example of this would be say you have \$20,000 in your checking account and want enough money for retirement. If you have 4% growth the number would start out small, but would increase as time went on. Decay rate is also important when trying to help an endangered species. A consequence would be if kids are studing this right now like we are not understanding this concept would hurt how well your future turns out. I agree completely with your teacher on this.

8. your teacher was talking about how important it was to invest in stock or in a retirement fund like your mom told you to do. this is because your money will grow and in the end you will have much more money than you started with