Modeling Exponential Functions (Percent Growth Decay)

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What is an exponential function?

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An exponential function is a mathematical function of the form f(x) = a * b^x, where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent. It represents growth or decay processes.

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What does it mean for a quantity to grow by a percentage?

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When a quantity grows by a percentage, it increases by that percentage of its current value. For example, a 10% growth means the new value is the original value plus 10% of the original value.

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CCSS.HSF-LE.A.1C

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What does it mean for a quantity to decay by a percentage?

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When a quantity decays by a percentage, it decreases by that percentage of its current value. For example, a 10% decay means the new value is the original value minus 10% of the original value.

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CCSS.HSF-LE.A.1C

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How do you write a function for exponential decay?

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A function for exponential decay can be written as V(t) = V0 * (1 - r)^t, where V0 is the initial value, r is the decay rate (as a decimal), and t is time.

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CCSS.HSF-IF.C.8B

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How do you write a function for exponential growth?

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A function for exponential growth can be written as V(t) = V0 * (1 + r)^t, where V0 is the initial value, r is the growth rate (as a decimal), and t is time.

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CCSS.HSF-LE.A.1A

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What is the formula for calculating the value of an investment after t years 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, P is the principal amount (initial investment), r is the annual interest rate (decimal), 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 simple interest and compound interest?

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Simple interest is calculated only on the principal amount, while compound interest is calculated on the principal and also on the accumulated interest from previous periods.

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CCSS.HSF.BF.A.2

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How do you convert a percentage to a decimal?

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To convert a percentage to a decimal, divide the percentage by 100. For example, 25% becomes 0.25.

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What is the initial value in an exponential function?

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The initial value in an exponential function is the value of the function when time (t) is zero. It represents the starting amount before any growth or decay occurs.

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CCSS.HSF.LE.B.5

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What does it mean for a population to decrease by a certain percentage each year?

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It means that each year, the population is reduced by that percentage of its current size. For example, a 5% decrease means the population is 95% of its size from the previous year.

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CCSS.HSF-LE.A.1C