Exponential Functions

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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 initial value in an exponential function represent?

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The initial value in an exponential function represents the value of the function when x = 0, which is equal to 'a' in the function f(x) = a(b)^x.

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What is the difference between exponential growth and exponential decay?

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Exponential growth occurs when the base 'b' is greater than 1, leading to an increase in value as x increases. Exponential decay occurs when the base 'b' is between 0 and 1, leading to a decrease in value as x increases.

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How do you identify the y-intercept of an exponential function?

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The y-intercept of an exponential function f(x) = a(b)^x is found by evaluating f(0), which equals 'a'.

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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 convert a percentage increase to a growth factor?

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To convert a percentage increase to a growth factor, use the formula: Growth Factor = 1 + (percentage increase / 100).

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How do you convert a percentage decrease to a decay factor?

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To convert a percentage decrease to a decay factor, use the formula: Decay Factor = 1 - (percentage decrease / 100).

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What is the formula for compound interest?

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The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

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What is the base of natural logarithms?

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The base of natural logarithms is 'e', approximately equal to 2.71828.