Which function increases at a faster rate on 0 to infinity, f(x) = x2 or g(x) = 2x? Explain your reasoning.

Answer:

The exponential function g(x) = 2^x increases at a faster rate than the quadratic function f(x) = x^2 over the interval [0, infinity). By comparing output values, such as f(x): 0, 1, 4, 9, 16 and g(x): 1, 2, 4, 8, 16, we see that the exponential function eventually doubles its way to much higher values. Because exponential growth (doubling) is multiplicative, it will always exceed the growth of a quadratic function as x increases.