Flashcard 4 Practice- Growth and Decay functions

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What is Linear Growth?

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Linear Growth refers to a situation where a quantity increases by a constant amount over equal intervals of time. For example, if a plant grows 2 cm every week, its growth is linear.

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What is Linear Decay?

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Linear Decay is when a quantity decreases by a constant amount over equal intervals of time. For example, if a bank account loses $50 every month, it is experiencing linear decay.

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What is Exponential Growth?

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Exponential Growth occurs when a quantity increases by a percentage of its current value over equal intervals of time. For example, if a population of bacteria doubles every hour, it is experiencing exponential growth.

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What is Exponential Decay?

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Exponential Decay is when a quantity decreases by a percentage of its current value over equal intervals of time. For example, if a radioactive substance loses 5% of its mass every hour, it is experiencing exponential decay.

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What is the formula for Linear Growth?

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The formula for Linear Growth can be expressed as y = mx + b, where m is the rate of growth, x is time, and b is the initial value.

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What is the formula for Linear Decay?

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The formula for Linear Decay can be expressed as y = -mx + b, where m is the rate of decay, x is time, and b is the initial value.

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What is the formula for Exponential Growth?

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The formula for Exponential Growth is y = a(1 + r)^t, where a is the initial amount, r is the growth rate, and t is time.

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What is the formula for Exponential Decay?

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The formula for Exponential Decay is 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 determine the number of deer in a population experiencing exponential decay?

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You can use the formula y = a(1 - r)^t, where a is the initial population, r is the decay rate, and t is the time in years.

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If Samantha's hair grows at a rate of 14% per week, what is the growth model?

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The growth model is y = 6(1.14)^x, where 6 is the initial length in inches and x is the number of weeks.