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.
My Answer: I have only been able to think of one example of exponential growth which is hair growth. From 2012, the length of hair someone's hair grows 50% each year. In 2012, the person's hair length was 12 inches.
I'm not sure what else I can do for the second one.Also, I'm not sure what I can come up with for exponential decay. Can someone please help me?
Thank you, in advance! :)
Hair does not grow that way. It grows at a fixed rate, it doesn't grow any faster for folks with long hair.
growth: Interest on money in a bank
bacteria
chicks
decay:
radioactivity
temperature of hot water in a cup.
Exponential growth and decay are present in various aspects of the real world. Here are additional examples for both exponential growth and decay:
Exponential Growth:
1. Population Growth: The population of a species, under favorable conditions and without any limiting factors, can exhibit exponential growth over time. For example, if a population of rabbits has abundant resources and no natural predators, their population can double every month.
2. Compound Interest: In finance, compound interest is a common example of exponential growth. When money is invested, the interest earned is added to the initial amount, and future interest is calculated based on the new total. Over time, this compounding effect leads to exponential growth in the overall investment value.
Exponential Decay:
1. Radioactive Decay: Many radioactive isotopes decay exponentially over time. For instance, carbon-14 dating is based on the exponential decay of carbon-14 isotopes in organic material to determine the age of artifacts and archaeological remains.
2. Drug Half-Life: The concept of half-life in pharmacology describes how drugs decrease in concentration within the body over time. Each drug has a specific half-life, and the concentration decreases by half at regular intervals. This process can be modeled using exponential decay.
I hope these examples help you understand exponential growth and decay in real-world scenarios!
Of course, I'd be happy to help you come up with more examples! Exponential growth and decay can be found in various aspects of the real world. Here are a few more examples:
Exponential Growth:
1. Population growth: When a population reproduces at a rate that exceeds the death rate, the population size can exhibit exponential growth. This is commonly seen in situations where resources are abundant, such as bacteria in a petri dish or the spread of certain invasive species.
2. Compound interest: In finance, when interest is compounded, the growth of an investment can follow an exponential pattern. For example, if you invest money in a savings account with a fixed interest rate, your balance will grow exponentially over time as the interest is added to the principal amount.
Exponential Decay:
1. Radioactive decay: Radioactive isotopes decay over time in an exponential manner. It follows a predictable pattern where the amount of radioactive substance decreases by a constant fraction over a fixed period. This is used in radiometric dating to determine the age of archaeological or geological samples.
2. Drug elimination from the body: When you take medication, the concentration of the drug in your bloodstream decreases exponentially as it gets metabolized and eliminated from your body. This allows healthcare professionals to calculate the appropriate dosing intervals for maintaining therapeutic levels.
To identify examples of exponential growth and decay in the real world, it can be helpful to think about situations where a quantity or value is increasing or decreasing at a constant percentage or fraction over time.