Unit 6: Flashcardziz #2 -Writing 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 amount in an exponential function represent?

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The initial amount 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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How do you identify the initial amount in the function g(x) = 200(1.25)^x?

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The initial amount is 200, which is the value of g(0) = 200(1.25)^0 = 200.

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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(b^x) where b > 1.

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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(b^x) where 0 < b < 1.

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How do you write an exponential function from a table of values?

Back

To write an exponential function from a table, identify the initial value and the growth/decay factor by examining the ratio of consecutive outputs.

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How do you simplify the expression (45x^6y^9) ÷ (5x^4y^2)?

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To simplify, divide the coefficients and subtract the exponents of like bases: 9x^2y^7.

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What is the result of simplifying the exponential expression 2^3 * 2^2?

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The result is 2^(3+2) = 2^5 = 32.

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What is the product of two exponential expressions with the same base?

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When multiplying two exponential expressions with the same base, you add the exponents: a^m * a^n = a^(m+n).