Which of these is an exponential function? \( y=\left(\frac{6}{5}\right)^{x} \quad y=\frac{4 x}{11} \)
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The Deep Dive
Exponential functions are characterized by having a variable in the exponent. In the function \( y=\left(\frac{6}{5}\right)^{x} \), the base is a constant, and the exponent is the variable \( x \), which makes it an exponential function. On the other hand, \( y=\frac{4 x}{11} \) is a linear function since \( x \) is in the numerator but not an exponent. To spot exponential functions, remember they often model growth or decay, such as population growth or radioactive decay. While linear functions graph as straight lines, exponential functions curve upwards (or downwards, in the case of decay) dramatically, illustrating their unique behavior in various real-life scenarios such as finance and science!