IM Algebra 2 - Unit 4 Mid Review

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What is an exponential decay function?

Back

An exponential decay function describes a process where a quantity decreases at a rate proportional to its current value. It can be expressed in the form: m(h) = m_0 * e^(-kt), where m_0 is the initial amount, k is the decay constant, and t is time.

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How do you write an exponential decay equation from a given initial amount and decay factor?

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To write an exponential decay equation, use the formula: m(t) = m_0 * (decay factor)^t, where m_0 is the initial amount and t is time.

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What is the decay factor if a substance decreases to 78% of its original amount every 2 hours?

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The decay factor is 0.78, meaning the amount remaining after each 2-hour interval is 78% of the previous amount.

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How do you determine the population change factor for a bacteria population that triples every hour?

Back

To find the population change factor for a half-hour, use the formula: change factor = (tripling factor)^(1/2) = 3^(1/2).

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What is the formula for exponential growth?

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The formula for exponential growth is f(t) = f_0 * e^(kt), where f_0 is the initial quantity, k is the growth rate, and t is time.

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How do you find the equation of an exponential function from a graph?

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To find the equation, identify the y-intercept and the growth/decay rate from the graph. Use the form y = a * b^x, where a is the y-intercept and b is the growth/decay factor.

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What does it mean for a population to triple every hour?

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It means that the population increases by a factor of 3 for every hour that passes.

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How do you express a population that triples every 10 years?

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The equation can be expressed as P(t) = P_0 * 3^(t/10), where P_0 is the initial population and t is time in years.

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What is the significance of the decay constant in exponential decay?

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The decay constant (k) indicates the rate at which the quantity decreases. A larger k means a faster decay.

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How do you calculate the decay factor for a given time interval?

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The decay factor can be calculated using the formula: decay factor = (initial amount) * (decay rate)^(time interval).