Exponential: Growth and Decay

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What is an exponential growth function?

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An exponential growth function is a mathematical expression that describes a quantity increasing at a constant percentage rate over time, typically represented as 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 an exponential decay function?

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An exponential decay function describes a quantity decreasing at a constant percentage rate over time, 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 write an expression for exponential growth after 't' time periods?

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The expression is y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is the number of time periods.

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How do you write an expression for exponential decay after 't' time periods?

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The expression is y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is the number of time periods.

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If a quantity doubles every week, what is the expression for its size after 't' weeks?

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The expression is y = a(2)^t, where 'a' is the initial size.

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What does a growth rate of 9% mean in an exponential function?

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A growth rate of 9% means that the quantity increases by 9% of its current value each time period, represented as y = a(1.09)^t.

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What does a decay rate of 20% mean in an exponential function?

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A decay rate of 20% means that the quantity decreases by 20% of its current value each time period, represented as y = a(0.8)^t.

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How do you evaluate an exponential function at a specific time?

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Substitute the value of 't' into the function and calculate the result.

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What is the formula to find the future value of an investment with compound interest?

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The formula is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years.

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What is the difference between linear growth and exponential growth?

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Linear growth increases by a constant amount over equal time intervals, while exponential growth increases by a constant percentage, leading to faster growth over time.