Determine whether the rule represents an exponential function. Explain why or why not. %0D%0A%0D%0A%0D%0A%0D%0A𝑦%0D%0A %0D%0A=%0D%0A %0D%0A12%0D%0A⋅%0D%0A %0D%0A3%0D%0A𝑥%0D%0Ay = 12⋅ 3 %0D%0Ax%0D%0A %0D%0A%0D%0A%0D%0A%0D%0AA%0D%0ASince the independent variable x is the exponent, 𝑦 = 12 ⋅ 3𝑥y\ =\ 12\ \cdot\ 3^xy = 12 ⋅ 3 %0D%0Ax%0D%0A does represent an exponential function. %0D%0A%0D%0AB%0D%0ASince the independent variable x is not the exponent, 𝑦 = 12 ⋅ 3𝑥y\ =\ 12\ \cdot\ 3^xy = 12 ⋅ 3 %0D%0Ax%0D%0A does not represent an exponential%0D%0A%0D%0Afunction.

Question

Determine whether the rule represents an exponential function. Explain why or why not. %0D%0A%0D%0A%0D%0A%0D%0A𝑦%0D%0A %0D%0A=%0D%0A %0D%0A12%0D%0A⋅%0D%0A %0D%0A3%0D%0A𝑥%0D%0Ay = 12⋅ 3 %0D%0Ax%0D%0A %0D%0A%0D%0A%0D%0A%0D%0AA%0D%0ASince the independent variable x is the exponent, 𝑦 = 12 ⋅ 3𝑥y\ =\ 12\ \cdot\ 3^xy = 12 ⋅ 3 %0D%0Ax%0D%0A  does represent an exponential function. %0D%0A%0D%0AB%0D%0ASince the independent variable x is not the exponent, 𝑦 = 12 ⋅ 3𝑥y\ =\ 12\ \cdot\ 3^xy = 12 ⋅ 3 %0D%0Ax%0D%0A  does not represent an exponential%0D%0A%0D%0Afunction.

GPT 3.5 · Answer

A. Since the independent variable x is the exponent in the equation y = 12 * 3^x, it does represent an exponential function.