Exponential Growth & Decay

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What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a consistent percentage over a period of time, leading to rapid increases as the quantity grows.

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What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over a period of time, leading to rapid decreases as the quantity diminishes.

Front

What is the formula for exponential growth?

Back

The formula is: N(t) = N0 * (1 + r)^t, where N0 is the initial amount, r is the growth rate, and t is time.

Front

What is the formula for exponential decay?

Back

The formula is: N(t) = N0 * (1 - r)^t, where N0 is the initial amount, r is the decay rate, and t is time.

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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 + growth rate)^number of periods.

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How do you calculate the future value of an asset with exponential decay?

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Use the formula: Future Value = Present Value * (1 - decay rate)^number of periods.

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What is the decay factor in exponential decay?

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The decay factor is calculated as (1 - r), where r is the decay rate.

Front

What is the growth factor in exponential growth?

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The growth factor is calculated as (1 + r), where r is the growth rate.

Front

If a population of 4000 mosquitoes grows at a rate of 25% per month, how many will there be after 4 months?

Back

There will be 9766 mosquitoes after 4 months.

Front

What is the initial value (y-intercept) in the function f(x)=13(0.27)^x?

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The initial value is 13.