Exponential Growth and Decay

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What is an exponential function?

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An exponential function is a mathematical function of the form f(x) = a(b)^x, where 'a' is a constant, 'b' is a positive real number, and 'x' is the exponent. It shows rapid growth or decay.

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What is exponential growth?

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Exponential growth occurs when a quantity increases by a consistent percentage over a period of time, resulting in a rapid increase.

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What is exponential decay?

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

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How do you identify an exponential growth function?

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An exponential growth function has a base greater than 1 in the expression f(x) = a(b)^x.

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How do you identify an exponential decay function?

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An exponential decay function has a base between 0 and 1 in the expression f(x) = a(b)^x.

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What does the base in an exponential function represent?

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The base in an exponential function represents the growth or decay factor. If the base is greater than 1, it indicates growth; if it is between 0 and 1, it indicates decay.

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What is the formula for calculating the future value of an investment with exponential growth?

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The formula 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 annual interest rate, and t is the time in years.

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If a population is modeled by P(t) = P0(1 + r)^t, what do P0, r, and t represent?

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P0 is the initial population, r is the growth rate (as a decimal), and t is the time in years.

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What is the percentage decrease in a quantity if it decays from 800 to 696?

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The percentage decrease is 13%.

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How do you calculate the percentage of decay in an exponential decay function?

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The percentage of decay can be calculated as (1 - decay factor) x 100%.