Exponential Growth and Decay Functions: A visual guide explaining the formula y = ab^x, with examples for growth (b > 1) and decay (0 < b < 1), including word problem interpretations and percentage changes.

A diagram illustrating exponential growth and decay functions, showing the formula y = ab^x with explanations for growth (b > 1) and decay (0 < b < 1), including word problem representations and examples.

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Show Answer Key & Explanations Step-by-step solution for: Exponential Growth and Decay Word Problems | Word problems, Word ...

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- The general form of an exponential function is y = a * b^x, where 'a' is the initial amount and 'b' is the growth or decay factor.
- For exponential growth, the base 'b' must be greater than 1 (b > 1). This can also be represented as b = 1 + r, where 'r' is the percent growth rate written as a decimal. The formula becomes y = a * (1 + r)^x.
- For exponential decay, the base 'b' must be between 0 and 1 (0 < b < 1). This can also be represented as b = 1 - r, where 'r' is the percent decay rate written as a decimal. The formula becomes y = a * (1 - r)^x.
- In the example given for decay, a 2% decrease per year means r = 0.02. Therefore, the decay factor is b = 1 - 0.02 = 0.98, and the function is y = a * (0.98)^x.

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