Exponential Functions: Reading Word Problems

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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. It describes growth or decay processes.

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What does the base 'b' in an exponential function represent?

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The base 'b' in an exponential function represents the growth (if b > 1) or decay (if 0 < b < 1) factor of the function.

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How do you identify exponential growth in a word problem?

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Exponential growth can be identified in a word problem by phrases indicating that a quantity increases by a consistent percentage over equal time intervals.

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What is the general form of an exponential growth equation?

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The general form of an exponential growth equation is y = a * (1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

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What is the difference between exponential growth and linear growth?

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Exponential growth increases at a rate proportional to its current value, while linear growth increases by a constant amount over time.

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How can you solve a word problem involving exponential decay?

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To solve a word problem involving exponential decay, identify the initial amount, the decay rate, and use the formula y = a * (1 - r)^t.

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What is the formula for exponential decay?

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The formula for exponential decay is y = a * e^(-kt), where 'a' is the initial amount, 'k' is the decay constant, and 't' is time.

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What does 'e' represent in exponential functions?

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The constant 'e' (approximately 2.718) is the base of natural logarithms and is used in continuous growth or decay models.

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How do you graph an exponential function?

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To graph an exponential function, plot points for various values of x, noting that the function approaches the x-axis (asymptote) but never touches it.

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What is a real-world example of exponential growth?

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A real-world example of exponential growth is population growth, where the population increases by a percentage each year.