To determine whether a given table represents an exponential growth function, an exponential decay function, or neither, you would typically examine how the values in the table change.
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Exponential Growth Function: As the independent variable (typically time) increases, the dependent variable (the value being measured) increases at an increasing rate. The values will grow larger and larger and, when plotted, the graph will show a curve that rises steeply.
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Exponential Decay Function: As the independent variable increases, the dependent variable decreases, approaching zero but never actually reaching it. The values will decrease at a decreasing rate, and, when plotted, the graph will show a curve that declines steeply and levels off.
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Neither: If the values do not consistently change in an exponential manner—meaning they don't consistently grow or decay at a constant rate—then the table represents neither.
To determine the nature of the table, look for patterns in the ratios of consecutive values or their differences:
- If each value is multiplied by a constant to get to the next, it suggests a growth or decay function.
- If the ratios of consecutive terms consistently increase, it's growth; if they consistently decrease, it's decay.
- If there's no consistent multiplicative factor, it's neither.
Please provide the specific values from the table so that a more precise determination can be made.