Exponential Functions Flashcard

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What is an exponential function?

Back

An exponential function is a mathematical function of the form y = a(b^x), where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent. It shows rapid growth or decay.

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What does the y-intercept of a function represent?

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The y-intercept of a function is the point where the graph of the function crosses the y-axis. It is the value of 'y' when 'x' is 0.

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How do you identify exponential growth?

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Exponential growth occurs when a quantity increases by a fixed percentage over equal time intervals, represented by a function of the form y = a(1 + r)^x, where 'r' is the growth rate.

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How do you identify exponential decay?

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Exponential decay occurs when a quantity decreases by a fixed percentage over equal time intervals, represented by a function of the form y = a(1 - r)^x, where 'r' is the decay rate.

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What is the formula for calculating compound interest?

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

Front

What does the base of an exponential function indicate?

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The base of an exponential function indicates the growth or decay factor. If the base is greater than 1, the function represents growth; if the base is between 0 and 1, it represents decay.

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What is the initial amount in an exponential function?

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The initial amount in an exponential function is the value of 'y' when 'x' is 0, represented by the constant 'a' in the function y = a(b^x).

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How do you determine the percentage increase from an exponential function?

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The percentage increase can be determined by subtracting 1 from the base of the exponential function (if in the form y = a(1 + r)^x) and multiplying by 100.

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

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The exponent in an exponential function indicates the number of time intervals that have passed, affecting the growth or decay of the quantity.

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How can you graph an exponential function?

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To graph an exponential function, plot points for various values of 'x', calculate the corresponding 'y' values, and connect the points to show the curve, which will rise or fall steeply.