To identify which feature is not a key aspect of the graph of the function \( A(t) = 3000(1.14)^t \), we can analyze the characteristics typically associated with exponential growth graphs.
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Exponential Growth: The function represents exponential growth because the growth factor (1.14) is greater than 1, leading to a rapid increase in value over time.
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Y-Intercept: At \( t = 0 \), \( A(0) = 3000(1.14)^0 = 3000 \). The graph will intersect the y-axis at \( (0, 3000) \).
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Asymptotic Behavior: As \( t \) approaches negative infinity, the value of \( A(t) \) approaches 0, but it will never be negative or zero (since the initial investment is positive).
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Continuous Growth: The function is continuously increasing, and there are no breaks or discontinuities in its domain.
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Domain and Range: The domain of the function is all non-negative real numbers (\( t \geq 0 \)) since it represents time, while the range is all values greater than 3000, tending towards infinity as \( t \) increases.
Now, if the question presents options regarding the properties of the graph, you can identify which one does not align with the characteristics mentioned above.
For example, if one of the options states that the graph can have negative values, that would not be a key feature, as the amount \( A(t) \) will never be negative.
Please provide the specific options you are considering so I can help you identify which one is not a key feature.
1 answer