Given an exponential function, say f(x), such that f(0) = 1 and f(1) = 2 and a quadratic finction, say g(x), such that g(0) = 0 and g(1) = 1.
The rate of change of a function f(x) over an interval
is given by
Thus, the rate of change (growth rate) of the exponential function, f(x) over the interval
is given by
Similarly, the rate of change (growth rate) of the quadratic function, g(x) over the interval
is given by
Therefore, the exponential grows at the same rate as the quadratic in the interval <span>.</span>
The rate of change of a function f(x) over an interval
is given by
Thus, the rate of change (growth rate) of the exponential function, f(x) over the interval
is given by
Similarly, the rate of change (growth rate) of the quadratic function, g(x) over the interval
is given by
Therefore, the exponential grows at the same rate as the quadratic in the interval <span>