How to interpret change in exponential models in word problems?

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Exponential models follow the general form y equals a times b to the x power. Here, a represents the initial value when x equals zero, b is the growth or decay factor that determines the rate of change, and x is typically the time variable. When b is greater than 1, we have exponential growth, shown by the blue curve. When b is between 0 and 1, we have exponential decay, shown by the red curve. The value of b determines how steep the curve is and whether it increases or decreases over time.