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

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What is exponential decay?

Back

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.

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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 \(\frac{12x^9y^4z^2}{24x^3y^4z^6}\)?

Back

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 \(\frac{x^6}{2z^4}\).

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What is an exponential regression equation?

Back

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.

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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.

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

Back

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.

Front

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

Back

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

Front

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

Back

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

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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.