Q2W4 Flashcard 2 Exponents / Growth / Decay

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What is Exponential Growth?

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Exponential Growth occurs when a quantity increases by a consistent percentage over a period of time. The general formula is A = P(1 + r)^t, where A is the amount after time t, P is the initial amount, r is the growth rate, and t is time.

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What is Exponential Decay?

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Exponential Decay occurs when a quantity decreases by a consistent percentage over a period of time. The general formula is A = P(1 - r)^t, where A is the amount after time t, P is the initial amount, r is the decay rate, and t is time.

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What is an asymptote?

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An asymptote is a line that a graph approaches but never touches. In exponential functions, the horizontal asymptote is often the x-axis (y = 0).

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What is the y-intercept of an exponential function?

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The y-intercept of an exponential function is the value of y when x = 0. For the function y = P(1 + r)^t, the y-intercept is P.

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How do you determine the range of an exponential function?

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The range of an exponential function is the set of possible output values. For functions of the form y = P(1 + r)^t, the range is y > 0 if P > 0.

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How do you classify exponential functions as growth or decay?

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If the base of the exponential function (1 + r) is greater than 1, it represents growth. If the base (1 - r) is less than 1, it represents decay.

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How do you convert scientific notation to standard form?

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To convert scientific notation to standard form, multiply the coefficient by 10 raised to the power indicated. For example, 3.5 x 10^4 = 35000.

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How do you compare numbers in scientific notation?

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To compare numbers in scientific notation, compare the exponents first. The number with the larger exponent is greater. If the exponents are the same, compare the coefficients.

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What is the formula for the area of a circle?

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The formula for the area of a circle is A = πr^2, where r is the radius of the circle.

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How do you write an equation for exponential decay?

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An equation for exponential decay can be written as y = P(1 - r)^t, where P is the initial amount and r is the decay rate.