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. 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 constant rate.

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What is the general form of an exponential function?

Back

The general form of an exponential function is f(x) = a(b)^x, where 'a' is the initial value, 'b' is the base (growth factor if b > 1, decay factor if 0 < b < 1), and 'x' is the exponent.

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What does the base 'b' represent in an exponential function?

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The base 'b' in an exponential function represents the growth or decay factor. If b > 1, it indicates growth; if 0 < b < 1, it indicates decay.

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How do you identify exponential growth from a function?

Back

Exponential growth can be identified if the base 'b' in the function f(x) = a(b)^x is greater than 1.

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How do you identify exponential decay from a function?

Back

Exponential decay can be identified if the base 'b' in the function f(x) = a(b)^x is between 0 and 1.

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What is the formula to calculate the future value in exponential growth?

Back

The formula to calculate future value in exponential growth is A = P(1 + r)^t, where A is the amount of money accumulated after n years, P is the principal amount, r is the rate of interest, and t is the time in years.

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If a quantity decreases by 20% each year, what is the decay factor?

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The decay factor is 0.80, which is calculated as 1 - 0.20.

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What is the value of a home worth today if it was purchased for $160,000 and appreciates at 5% per year for 20 years?

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The home is worth approximately $424,527.63 today.

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What type of function is represented by y = 7(5/4)^x?

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This function represents Exponential Growth because the base (5/4) is greater than 1.