Exponential Growth and Decay

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What is Exponential Growth?

Back

Exponential Growth occurs when a quantity increases by a constant percentage over a period of time. The general formula is: y = 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 Exponential Decay?

Back

Exponential Decay occurs when a quantity decreases by a constant percentage over a period of time. The general formula is: y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

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What does the variable 'a' represent in exponential functions?

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'a' represents the initial amount or starting value before any growth or decay occurs.

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What does the variable 'r' represent in exponential functions?

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'r' represents the rate of growth (if positive) or decay (if negative) expressed as a decimal.

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How do you identify an exponential growth function?

Back

An exponential growth function has a base greater than 1 in the form y = a(b)^x, where b > 1.

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How do you identify an exponential decay function?

Back

An exponential decay function has a base between 0 and 1 in the form y = a(b)^x, where 0 < b < 1.

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What is the formula to calculate the amount remaining after exponential decay?

Back

The formula is: y = a(1 - r)^t, where 'y' is the remaining amount, '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 will it be after 2 years?

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Using the formula y = a(1 + r)^t: y = 1000(1 + 0.10)^2 = 1000(1.1)^2 = 1210.

Front

What is the common ratio in the function f(x) = 200(0.5)^x?

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The common ratio is 0.5, indicating a decay of 50%.

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What is the equation for a population that doubles every year?

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The equation is y = a(2)^t, where 'a' is the initial population.