Algebra 2 Unit 1 Topic 3 Review

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What is an exponential decay function?

Back

An exponential decay function is a mathematical function of the form f(x) = a(b)^x, where 0 < b < 1. It represents a quantity that decreases over time.

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How can you identify an exponential decay function from its equation?

Back

You can identify an exponential decay function by checking if the base of the exponent (b) is less than 1.

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What is the general form of an exponential growth function?

Back

The general form of an exponential growth function is f(x) = a(b)^x, where b > 1.

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What does the initial amount represent in an exponential function?

Back

The initial amount represents the value of the function when x = 0, denoted as 'a' in the function f(x) = a(b)^x.

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How do you calculate the future value of an investment with exponential growth?

Back

You can calculate the future value using the formula: Future Value = Initial Amount * (1 + growth rate)^t.

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What is the formula for calculating the value of an investment that grows by a percentage each year?

Back

The formula is: y = P(1 + r)^t, where P is the initial amount, r is the growth rate, and t is the time in years.

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What is an asymptote in the context of exponential functions?

Back

An asymptote is a line that a graph approaches but never touches. For exponential functions, the horizontal asymptote is often y = 0.

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What is the range of the function y = 2^x?

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The range of the function y = 2^x is (0, ∞), meaning it can take any positive value.

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What happens to the value of an exponential decay function as x approaches infinity?

Back

As x approaches infinity, the value of an exponential decay function approaches 0.

Front

What is the significance of the base in an exponential function?

Back

The base determines the rate of growth or decay. A base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.