Exponential Functions Review

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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 the base (a positive real number), and 'x' is the exponent.

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How can you identify an exponential function from a list of functions?

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An exponential function has a variable in the exponent. For example, f(x) = 3^x is exponential, while f(x) = 3x^2 is not.

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What is the common ratio in an exponential function?

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The common ratio, often denoted as 'b', is the factor by which the function's value multiplies for each unit increase in 'x'.

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What does it mean for a function to exhibit exponential growth?

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Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to rapid increases over time.

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What does it mean for a function to exhibit exponential decay?

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Exponential decay occurs when a quantity decreases at a rate proportional to its current value, leading to rapid decreases over time.

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What is the y-intercept of an exponential function?

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The y-intercept of an exponential function f(x) = a * b^x is the value of 'a', which is the function's value when x = 0.

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If a bank offers 2.5% simple interest, how do you calculate the interest earned?

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Interest earned = Principal * Rate * Time. For example, for $5,000 at 2.5% for 3 years: $5000 * 0.025 * 3 = $375.

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What is the difference between linear and exponential functions?

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Linear functions have a constant rate of change, while exponential functions have a variable rate of change that increases or decreases rapidly.

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What is the formula for exponential growth?

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The formula for exponential growth is f(t) = a * e^(rt), where 'a' is the initial amount, 'e' is Euler's number, 'r' is the growth rate, and 't' is time.

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What is the formula for exponential decay?

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The formula for exponential decay is f(t) = a * e^(-rt), where 'a' is the initial amount, 'e' is Euler's number, 'r' is the decay rate, and 't' is time.