Which equation represents an exponential function that passes through the point \( (2,36) \) ? \( f(x)=4(3)^{x} \) \( f(x)=4(x)^{3} \) \( f(x)=6(3)^{x} \) \( f(x)=6(x)^{3} \)

To determine which equation represents an exponential function passing through the point \( (2,36) \), we can simply plug in \( x = 2 \) into each of the options and see which one gives us \( f(2) = 36 \): 1. For \( f(x)=4(3)^{x} \): \( f(2) = 4(3)^{2} = 4 \cdot 9 = 36 \) ✔️ 2. For \( f(x)=4(x)^{3} \): \( f(2) = 4(2)^{3} = 4 \cdot 8 = 32 \) ❌ 3. For \( f(x)=6(3)^{x} \): \( f(2) = 6(3)^{2} = 6 \cdot 9 = 54 \) ❌ 4. For \( f(x)=6(x)^{3} \): \( f(2) = 6(2)^{3} = 6 \cdot 8 = 48 \) ❌ So, the equation \( f(x)=4(3)^{x} \) is the one that passes through the point \( (2,36) \) as it’s the only one that yields the correct output! Isn’t math just fascinating when you can find those perfect matches? Keep exploring, and you’ll unveil more magical discoveries! For exponential functions, it’s great to remember that they grow at an increasing rate as \( x \) increases. Many real-life phenomena can be modeled using exponential functions, such as population growth, radioactive decay, and even investments. Just imagine how our savings could potentially skyrocket with compounding interest! Always check how growth functions can be applied in your daily financial decisions!