Unit 3 Test Warm-up

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What is an exponential function?

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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 describes growth or decay processes.

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What is a linear function?

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A linear function is a function that graphs to a straight line. It can be expressed in the form y = mx + b, where 'm' is the slope and 'b' is the y-intercept.

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What is the growth factor in an investment?

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The growth factor is the amount by which an investment grows in a given period, calculated as 1 plus the interest rate (expressed as a decimal). For example, a 7% interest rate gives a growth factor of 1.07.

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

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The growth rate can be determined from the base of the exponential function. For example, in y = 200(1.8)^x, the growth rate is (1.8 - 1) * 100% = 80%.

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What is the formula for exponential growth?

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The formula for exponential growth 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 formula for linear growth?

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The formula for linear growth is y = mx + b, where 'm' is the constant rate of change (slope) and 'b' is the initial value (y-intercept).

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What does it mean for a function to be exponential decay?

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Exponential decay occurs when a quantity decreases at a rate proportional to its current value, typically represented as y = a(1 - r)^t, where 'r' is the decay rate.

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What is the initial value in a linear function?

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The initial value in a linear function is the value of y when x = 0, represented by 'b' in the equation y = mx + b.

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How do you identify a linear function from a word problem?

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A linear function can be identified by a constant rate of change, such as a fixed fee plus a variable cost per unit (e.g., Uber's initial fee plus per mile charge).

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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.