4)) Both of these functions grow as \( x \) gets larger and larger. Which function eventually exceeds the other? \( f(x)=15 x+9 \) \( g(x)=3(4)^{x} \) Submit

We have two functions:   f(x) = 15x + 9        (Linear)   g(x) = 3(4)^x        (Exponential) Exponential functions grow much more quickly than linear functions. Although f(x) might be larger for some small values of x, as x increases, g(x) eventually exceeds f(x) and remains larger thereafter. For example, at x = 0:   f(0) = 15(0) + 9 = 9   g(0) = 3(4)^0 = 3 Here, f(0) > g(0). At x = 1:   f(1) = 15(1) + 9 = 24   g(1) = 3(4)^1 = 12 Still, f(1) > g(1). At x = 2:   f(2) = 15(2) + 9 = 39   g(2) = 3(4)^2 = 3(16) = 48 Now f(2) < g(2). From this, you can see that although f(x) starts out larger, g(x) eventually exceeds it and continues to grow dramatically faster. Answer: g(x) eventually exceeds f(x).