Which of these is an exponential function? \( y=0.5^{x} \quad y=3 x+5 \)
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Bonus Knowledge
Exponential functions are characterized by having a constant base raised to a variable exponent. In this case, \( y=0.5^{x} \) is an exponential function because the variable \( x \) is in the exponent, while \( y=3x+5 \) is a linear function with respect to \( x \). Exponential functions, like \( y=0.5^{x} \), can model real-world scenarios such as population growth, radioactive decay, or even your favorite viral TikTok video! They can take off rapidly or decline sharply, showcasing their unique ability to depict change over time in different contexts.