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.
Exponential growth and decay are present in various aspects of the real world.
Examples of exponential growth:
1. Population growth: The world's population has been growing exponentially over the past few centuries, with the rate of growth accelerating due to advancements in healthcare, technology, and food production.
2. Compound interest: In finance, investments can grow exponentially over time through compound interest, where the interest is added to the principal amount, leading to exponential growth in the investment's value.
Examples of exponential decay:
1. Radioactive decay: Radioactive materials decay exponentially over time, as the unstable isotopes lose their radioactivity and transform into more stable elements.
2. Drug concentration in the body: When a person takes medication, the concentration of the drug in their body typically decreases exponentially over time as the drug is metabolized and eliminated from the system.
can you do a growth and decay for drug concentration in the body
Sure!
Example of exponential growth for drug concentration in the body:
1. Let's say a person takes a medication that has a half-life of 4 hours. Initially, the drug concentration in their body is 100 mg/ml. After 4 hours, the concentration will double to 200 mg/ml, after another 4 hours it will double again to 400 mg/ml, and so on. This exponential growth in drug concentration continues as the medication is absorbed and accumulates in the body.
Example of exponential decay for drug concentration in the body:
2. Following the example above, if the person stops taking the medication, the drug concentration in their body will start to decrease exponentially over time. After another 4 hours (total 8 hours since the last dose), the concentration will decrease to 200 mg/ml, after another 4 hours it will decrease to 100 mg/ml, and so on. The drug concentration will continue to decrease exponentially as the medication is metabolized and eliminated from the body.
can you put this in a more simpler way
Certainly!
Growth example: If someone takes a medication that doubles in concentration every 4 hours, the drug concentration in their body will keep increasing rapidly over time.
Decay example: If someone stops taking a medication that decreases in concentration by half every 4 hours, the drug concentration in their body will decrease quickly as the medication is metabolized and eliminated.