GGG Review

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What is exponential decay?

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Exponential decay is a decrease in a quantity that follows the formula: \(N(t) = N_0 e^{-kt}\), where \(N_0\) is the initial amount, \(k\) is the decay constant, and \(t\) is time.

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How do you calculate the value after a certain number of years with a decay rate?

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To calculate the value after a certain number of years with a decay rate, use the formula: \(V = V_0 (1 - r)^t\), where \(V_0\) is the initial value, \(r\) is the decay rate, and \(t\) is the time in years.

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What is scientific notation?

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Scientific notation is a way of expressing numbers as a product of a number between 1 and 10 and a power of 10, e.g., \(5.23 \times 10^7\).

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How do you convert a number to scientific notation?

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To convert a number to scientific notation, move the decimal point to create a number between 1 and 10, and count the number of places moved to determine the exponent of 10.

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What is the formula for the diagonal of a rectangle?

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The formula for the diagonal \(d\) of a rectangle with length \(l\) and width \(w\) is: \(d = \sqrt{l^2 + w^2}\).

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What is the initial value in a decay problem?

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The initial value in a decay problem is the starting amount before any decay has occurred, often denoted as \(V_0\).

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How do you simplify a fraction in scientific notation?

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To simplify a fraction in scientific notation, divide the coefficients and subtract the exponents: \(\frac{a \times 10^m}{b \times 10^n} = \frac{a}{b} \times 10^{m-n}\).

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What is the decay rate?

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The decay rate is the percentage at which a quantity decreases over a specific period, often expressed as a decimal in calculations.

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How do you find the time it takes for a value to decay to a certain amount?

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To find the time it takes for a value to decay to a certain amount, rearrange the decay formula to solve for \(t\): \(t = \frac{\ln(V/V_0)}{\ln(1 - r)}\).

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What is the significance of the exponent in scientific notation?

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The exponent in scientific notation indicates the number of places the decimal point has moved, determining the scale of the number.