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, resulting in a rapid increase. For example, if a population grows by 10% each year, it will grow faster each subsequent year.

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What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over time, leading to a rapid decrease. For example, radioactive substances decay at a rate proportional to their current amount.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is f(t) = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

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What is the formula for exponential decay?

Back

The formula for exponential decay is f(t) = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

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How do you identify exponential growth from a graph?

Back

Exponential growth is identified by a curve that rises steeply as it moves to the right, indicating that the quantity increases rapidly over time.

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How do you identify exponential decay from a graph?

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Exponential decay is identified by a curve that falls steeply as it moves to the right, indicating that the quantity decreases rapidly over time.

Front

What is the initial value in the function f(x) = 300(1.16)^x?

Back

The initial value is 300, which represents the starting amount before any growth occurs.

Front

If a quantity doubles every 5 years, what is the growth factor?

Back

The growth factor is 2, meaning the quantity increases to twice its size every 5 years.

Front

What is the half-life in the context of exponential decay?

Back

Half-life is the time required for a quantity to reduce to half its initial value. It is a common concept in radioactive decay.

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How do you calculate the future value of an investment with exponential growth?

Back

Use the formula: Future Value = Present Value * (1 + r)^t, where 'r' is the growth rate and 't' is the number of years.