Exponential Functions and Log

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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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What does the base of an exponential function represent?

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The base of an exponential function indicates the growth (if greater than 1) or decay (if between 0 and 1) rate of the function.

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What is the general form of an exponential growth function?

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The general form of an exponential growth function is f(x) = a * (1 + r)^x, where 'r' is the growth rate.

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What is the general form of an exponential decay function?

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The general form of an exponential decay function is f(x) = a * (1 - r)^x, where 'r' is the decay rate.

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How do you calculate the half-life of a substance?

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The half-life can be calculated using the formula t(1/2) = ln(2) / k, where 'k' is the decay constant.

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What does the term 'logarithm' mean?

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A logarithm is the inverse operation to exponentiation, indicating the power to which a base must be raised to obtain a given number.

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What is the change of base formula for logarithms?

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The change of base formula states that log_b(a) = log_k(a) / log_k(b) for any positive base k.

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What is the value of log_2(8)?

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log_2(8) = 3, because 2^3 = 8.

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What does the term 'common ratio' refer to in exponential functions?

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The common ratio is the factor by which a quantity increases or decreases in each time period in a geometric sequence.

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How do you determine the number of intervals in a decay problem?

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To determine the number of intervals, divide the total time by the time per interval.