An exponential growth function can be expressed as \( y = 2^x \). The general form of an exponential function is \( y = a \cdot b^x \), where "a" represents the initial value and "b" denotes the growth factor. In this particular function, "b" is 2, which is greater than 1, signifying that this is indeed an example of exponential growth. This means that as "x" increases by one unit, the value of "y" is multiplied by 2, resulting in a rapidly increasing output. A key point about exponential growth is that, although the growth rate remains constant, the actual increase in value becomes larger as the independent variable "x" continues to rise. When graphing the function, one can observe that an exponential growth function produces a curve that rises steeply upwards as "x" increases.
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An exponential growth function is: y = 2^x. Explanation: Form of an exponential function:The general form of an exponential function is y = a * b^x, where "a" is the initial value and "b" is the growth factor. Growth factor greater than 1:In this function, "b" is 2, which is greater than 1, signifying exponential growth. This means that as "x" increases by 1 unit, the value of "y" is multiplied by 2, leading to a rapidly increasing output. Key points about exponential growth: Constant growth rate:The growth rate in an exponential function remains constant, but the actual increase in value becomes larger as the independent variable (x) increases. Graphing the function:When plotted, an exponential growth function will show a curve that rapidly rises upwards as x increases.
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