Exponential functions on the real numbers
Evaluate and interpret exponential functions at non-integer inputs.
In A2 students considered exponential functions at integer inputs only. Now that they understand how to determine the value of $b^x$ for any rational number $x$, they can approximate $b^x$ to any degree of accuracy for any real number $x$. In this section they broaden their view of exponential functions to include the entire real number line as a possible domain. They evaluate functions and interpret their values at real inputs in terms of a context, in preparation for the more sophisticated work in the following sections.