Part 1: How are exponential growth and decay present in the real world? Give at least 2 examples for exponential growth and 2 examples of exponential decay.
Part 2: View and comment on the work of at least 2 other students. Try to choose students whose work is based on different real-world examples than the ones you chose.
Part 1:
Exponential growth is present in various aspects of the real world. Two examples of exponential growth are:
1) Population growth: In many countries, the population grows at an exponential rate due to factors such as increasing birth rates and decreasing mortality rates. As the population grows, there is a compounding effect as more people are added to the base population, leading to exponential growth.
2) Compound interest: In the finance world, compound interest is an example of exponential growth. When money is invested with an interest rate that compounds, the interest earned in a given period is added to the initial amount, and then the new total becomes the principal for the next period. This compounding effect results in exponential growth of the investment over time.
On the other hand, exponential decay also exists in various phenomena. Two examples of exponential decay are:
1) Radioactive decay: Radioactive substances decay over time following an exponential decay pattern. The rate of decay is constant and proportional to the amount of the substance remaining. As time passes, the substance's activity decreases exponentially.
2) Drug concentration in the body: When a person takes medication, the concentration of the drug in their body starts to decline exponentially. The drug is metabolized and eliminated from the body at a constant rate, causing a exponential decrease in its concentration.
Part 2:
Student 1: I liked your examples of exponential growth in population and compound interest. They are both classic examples that clearly demonstrate the concept. I also appreciated how you explained the compounding effect in compound interest. It really helps to understand how small increments can lead to exponential growth over time.
Student 2: Your examples of exponential decay in radioactive decay and drug concentration are very relevant. Radioactive decay is a natural process that we often encounter in our lives, and the exponential decay pattern is fascinating. Similarly, drug concentration in the body is something most people can relate to, and it's interesting how the body metabolizes and eliminates drugs. Overall, your examples effectively illustrate the concept of exponential decay in real-world scenarios.