Q2: Pre-AP Alg2 Review Questions for Retake Flashcard#1 U1L1.4-L1.5

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What is exponential decay?

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Exponential decay is a decrease in a quantity that follows an exponential function, typically represented as \(y = a(1 - r)^t\), where \(a\) is the initial amount, \(r\) is the decay rate, and \(t\) is time.

Tags

CCSS.HSF-IF.C.8B

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How do you calculate the population after a certain number of years with exponential decay?

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To calculate the population after a certain number of years with exponential decay, use the formula \(P = P_0(1 - r)^t\), where \(P_0\) is the initial population, \(r\) is the decay rate, and \(t\) is the number of years.

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What is the formula for depreciation?

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The formula for depreciation is \(V = P(1 - r)^t\), where \(V\) is the value after depreciation, \(P\) is the initial value, \(r\) is the depreciation rate, and \(t\) is the time in years.

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How do you simplify the expression \(\frac{12x^9y^4z^2}{24x^3y^4z^6}\)?

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To simplify, divide the coefficients and subtract the exponents: \(\frac{12}{24} = \frac{1}{2}\), \(x^{9-3} = x^6\), \(y^{4-4} = 1\), \(z^{2-6} = z^{-4}\). The simplified expression is \(\frac{x^6}{2z^4}\).

Tags

CCSS.HSA.APR.A.1

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What is an exponential regression equation?

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An exponential regression equation is a model that describes data that grows or decays exponentially, typically in the form \(Y = ab^x\), where \(a\) is the initial value, \(b\) is the growth/decay factor, and \(x\) is the independent variable.

Tags

CCSS.HSF-LE.A.1A

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What does a 6% decrease per year mean in terms of population?

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A 6% decrease per year means that each year, the population is reduced to 94% of its value from the previous year.

Tags

CCSS.HSF-LE.A.1C

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How do you find the value of an asset after a certain number of years of depreciation?

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To find the value of an asset after depreciation, use the formula \(V = P(1 - r)^t\), substituting the initial value, depreciation rate, and time.

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What is the significance of the initial value in exponential functions?

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The initial value in exponential functions represents the starting amount before any growth or decay occurs.

Tags

CCSS.HSF-IF.C.8B

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How do you interpret the decay rate in a population model?

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The decay rate indicates the percentage by which the population decreases each year, affecting how quickly the population declines.

Tags

CCSS.HSF-IF.C.8B

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What is the relationship between exponential functions and logarithms?

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Exponential functions and logarithms are inverses of each other; the logarithm of a number is the exponent to which the base must be raised to produce that number.

Tags

CCSS.HSF.BF.B.5