Exponential Growth and 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, resulting in a rapid increase. Example: If a population of bacteria doubles every hour, it exhibits exponential growth.

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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 a rapid decrease. Example: A radioactive substance that loses half of its mass every 5 years shows exponential decay.

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How do you identify Exponential Growth in a function?

Back

In a function of the form A = a(1 + r)^t, if r > 0, it represents exponential growth. Example: A = 100(1.05)^t shows growth.

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How do you identify Exponential Decay in a function?

Back

In a function of the form A = a(1 - r)^t, if r > 0, it represents exponential decay. Example: A = 200(0.9)^t shows decay.

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What does the variable 'a' represent in an exponential function?

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The variable 'a' represents the initial amount or starting value in an exponential function. Example: In f(x) = 500(1.2)^x, '500' is the initial amount.

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Convert 20% to a decimal.

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0.20

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Convert 75% to a decimal.

Back

0.75

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What is the formula for exponential growth?

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The formula for exponential growth is A = a(1 + r)^t, where A is the amount after time t, 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?

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The formula for exponential decay is A = a(1 - r)^t, where A is the amount after time t, a is the initial amount, r is the decay rate, and t is time.

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If a population of 1000 increases by 10% each year, what is the population after 2 years?

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Population after 2 years = 1000(1.10)^2 = 1210.