12/03 - CTG: Exponential Functions Review

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What is an exponential function?

Back

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

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What is a horizontal asymptote?

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A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity. For exponential decay functions, the horizontal asymptote is typically y = 0.

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How do you determine the growth rate in an exponential function?

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The growth rate in an exponential function is determined by the base 'b' in the function f(x) = a(b)^x. If b > 1, the function represents growth; if 0 < b < 1, it represents decay.

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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 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.

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What does it mean for a function to be increasing?

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A function is increasing if, as the input (x) increases, the output (f(x)) also increases. In exponential functions, this occurs when the base 'b' is greater than 1.

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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 f(0), which equals 'a'. It represents the initial value of the function when x = 0.

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How do you model exponential decay?

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Exponential decay can be modeled using the function f(t) = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

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What is the difference between linear and exponential growth?

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Linear growth increases by a constant amount over equal intervals, while exponential growth increases by a constant percentage over equal intervals, leading to faster growth as time progresses.

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

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The base in an exponential function determines the rate of growth or decay. A base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

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How can you identify an exponential function from a table of values?

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An exponential function can be identified from a table of values if the ratio of consecutive outputs remains constant or if the percentage change between outputs is constant.