The general formula for an exponential function is f(x) = ae^rt while the general form of a quadratic equation is f(x) = ax^2 + bx + c
Thus,
f(x) = 7e^0.5x is an exponential function and
g(x) = 3x^2 + 7x - 4 is a quadratic function
Let us substitute values of x into each function and compare the growth rates
For x = 1,
f(1) = 7e^0.5 = 11.4
g(1) = 3(1)^2 + 7(1) - 4 = 3 + 7 - 4 = 6
For x = 2,
f(1) = 7e^2(0.5) = 19
g(1) = 3(2)^2 + 7(2) - 4 = 12 + 14 - 4 = 22
For x = 3,
f(3) = 7e^3(0.5) = 31
g(1) = 3(3)^2 + 7(3) - 4 = 27 + 21 - 4 = 44
We can see that g(x) is increasing at a faster rate than f(x).