EOC Category 5 - Exponential Functions

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What is an exponential function?

Back

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 represents growth or decay processes.

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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 determines the rate of growth (if b > 1) or decay (if 0 < b < 1).

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What is the initial value in the function f(x) = 300(1.16)^x?

Back

The initial value is 300, which represents the value of the function when x = 0.

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How do you identify exponential growth?

Back

Exponential growth occurs when 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?

Back

Exponential decay occurs when the base 'b' in the function f(x) = a(b)^x is between 0 and 1.

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What is the function that models a 2% annual decrease in value from an initial amount of $100,000?

Back

The function is f(x) = 100,000(0.98)^x.

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If a population increases by 10% each year, what is the growth factor?

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The growth factor is 1.10.

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

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The formula is f(x) = a(1 + r)^x, where 'a' is the initial amount, 'r' is the growth rate, and 'x' is the number of time periods.

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

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The formula is f(x) = a(1 - r)^x, where 'a' is the initial amount, 'r' is the decay rate, and 'x' is the number of time periods.

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How do you calculate the population after 2 years if the current population is 100,000 and it grows by 10% per year?

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The population after 2 years is calculated as f(2) = 100,000(1.10)^2.