PH: L3.5 Exponential and Logarithmic Models

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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 is the base of a logarithm?

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The base of a logarithm is the number that is raised to a power to obtain a given number. For example, in log_b(a) = c, b is the base.

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What is the relationship between exponential and logarithmic functions?

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Exponential functions and logarithmic functions are inverses of each other. If y = b^x, then x = log_b(y).

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What is the natural logarithm?

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The natural logarithm is the logarithm to the base e, where e is approximately equal to 2.71828. It is denoted as ln(x).

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What is the common logarithm?

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The common logarithm is the logarithm to the base 10, denoted as log(x).

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How do you solve an exponential equation?

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To solve an exponential equation, you can take the logarithm of both sides, use properties of logarithms, and isolate the variable.

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What is the exponential growth model?

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The exponential growth model describes a situation where the growth rate of a quantity is proportional to its current value, often expressed as P(t) = P_0 * e^(rt).

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What is the exponential decay model?

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The exponential decay model describes a situation where a quantity decreases at a rate proportional to its current value, often expressed as P(t) = P_0 * e^(-rt).

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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 k.

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What is the product rule for logarithms?

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The product rule states that log_b(xy) = log_b(x) + log_b(y).