Science:Math Exam Resources/Courses/MATH110/April 2013/Question 02 (d)/Solution 1

Any exponential function of the form $f(x)=a^{x}$, where $a$ is a real number, will satisfy the equation above because $\displaystyle f'(x)=\ln(a)a^{x}=kf(x)$ for k = ln(a). One example would be our favorite $f(x)=e^{x}$. Here k = ln(e) = 1 and a graph is shown below.