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.
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Exponential growth and decay are phenomena commonly observed in the real world. Here are two examples of exponential growth and two examples of exponential decay:
Exponential Growth:
1. Population Growth: The human population on Earth demonstrates exponential growth, where population size increases at a rate proportional to the current population size. As more people are born, they contribute to the overall population, resulting in an accelerating growth rate.
2. Compound Interest: In finance, when interest is compounded, the amount of money in an account or investment increases exponentially. This occurs because the interest earned in each period is added to the principal, and subsequently, future interest is calculated based on the new total.
Exponential Decay:
1. Radioactive Decay: Radioactive elements decay over time, with the rate of decay being proportional to the amount of radioactive material remained. As time passes, the quantity of radioactive material reduces exponentially until it reaches stability.
2. Medicine Decaying in the Body: When you take medication, the concentration of the active ingredients in your body decreases exponentially over time. As the body metabolizes and eliminates the drugs, the drug concentration decreases at a rate determined by the drug's half-life, leading to a decay-like behavior.