Exponential Growth and Decay

Front

What is Exponential Growth?

Back

Exponential Growth occurs when a quantity increases by a consistent percentage over a period of time, leading to rapid growth. Example: A population of bacteria doubles every hour.

Front

What is Exponential Decay?

Back

Exponential Decay occurs when a quantity decreases by a consistent percentage over time, leading to rapid decline. Example: A radioactive substance decaying over time.

Front

What is the formula for Exponential Growth?

Back

y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

What is the formula for Exponential Decay?

Back

y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

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How does Exponential Growth differ from Linear Growth?

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Exponential Growth increases at a rate proportional to its current value, while Linear Growth increases by a fixed amount.

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How does Exponential Decay differ from Linear Decay?

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Exponential Decay decreases at a rate proportional to its current value, while Linear Decay decreases by a fixed amount.

Front

What is a real-world example of Exponential Growth?

Back

The spread of a viral infection, where each infected person infects multiple others.

Front

What is a real-world example of Exponential Decay?

Back

The depreciation of a car's value over time.

Front

If a population of 1000 grows at a rate of 10% per year, what will it be after 3 years?

Back

After 3 years, the population will be approximately 1331.

Front

If a substance has a half-life of 5 years, how much of a 100g sample remains after 15 years?

Back

After 15 years, 12.5g of the substance remains.