APPC Unit 2A Review

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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 a positive real number, and 'x' is the variable. It describes growth or decay processes.

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How do you write the function for a given table of values?

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To write the function for a table of values, identify the pattern in the data points, determine if it follows a linear, quadratic, or exponential trend, and then derive the function accordingly.

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What is the half-life in the context of exponential decay?

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Half-life is the time required for a quantity to reduce to half its initial value. In exponential decay, it is a constant rate at which the quantity decreases.

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What does the limit of a function as x approaches infinity represent?

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The limit of a function as x approaches infinity represents the value that the function approaches as the input grows larger and larger.

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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 'a' is the initial value and 'b' is the growth factor (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 'a' is the initial value and '0 < b < 1' is the decay factor.

Tags

CCSS.HSF-IF.C.8B

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How do you determine 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'.

Tags

CCSS.HSF-IF.C.7E

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

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The base of 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.

Tags

CCSS.HSF-IF.C.8B

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How do you find the number of bacteria after a certain time given a half-life?

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To find the number of bacteria after a certain time, use the formula: N(t) = N0 * (1/2)^(t/T), where N0 is the initial amount, t is the elapsed time, and T is the half-life.

Tags

CCSS.HSF.LE.A.4