Algebra II - Growth and Decay Factor

For an annual rate of change of -31%, find the corresponding growth or decay factor

Comments for Algebra II - Growth and Decay Factor

 Apr 05, 2011 Algebra II - Growth and Decay Factor by: Staff The question: For an annual rate of change of -31%, find the corresponding growth or decay factor The answer: The annual rate of change for your problem is a constant: -31% per year. The function which describes a constant % rate of change is called an exponential function. It has the form: f(t) = (initial value)*(1 + rate of change)^t ------------------------------------------------------------ Definitions: t = time in years (1 + rate of change) is called the “growth factor” if its value is greater than 1. (1 + rate of change) is called the “decay factor” if its value is less than 1, but greater than 0. (1 + rate of change)^t = (1 + rate of change) raised to the “t” power ------------------------------------------------------------ For your problem f(t) = (initial value)*(1 + rate of change)^t f(t) = (initial value)*(1 – 31%)^t f(t) = (initial value)*(1 – .31)^t f(t) = (initial value)*(0.69)^t (1 + rate of change) = 0.69 < 1 = decay factor The decay factor is: 0.69 The final answer: The decay factor is: 0.69 Thanks for writing. Staff www.solving-math-problems.com

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