Final answer:
The equation of an exponential function is typically in the form f(x) = ab^x, where 'a' is the initial value and 'b' is the base related to growth or decay.
Step-by-step explanation:
To find the equation of an exponential function, we typically use the form f(x) = ab^x, where 'a' is the initial value (y-intercept), 'b' is the base of the exponential function, and 'x' is the variable. When given two points that the function must pass through, we can set up a system of equations and solve for 'a' and 'b'. For instance, if we have a point (0, y0) and another point (x1, y1), the equations would be a = y0 and ab^x1 = y1, and we'd solve for 'b' using these equations. If we're dealing with growth or decay and know the rate and time frame, we can use formulas such as Eq. 1.2 from the reference material to find 'b'.