Generalized Solution for RC Switching

RC circuits will go exponentially from some initial voltage to a final voltage. We can formulate a general exponential switching function:

$$\begin{array}{r}V(t)=V_{\text{final}}+(V_{\text{initial}}-V_{\text{final}})\cdot \exp \left(-\frac{t-t_0}{\tau }\right)\\ V(t)=V_{\text{final}}-(V_{\text{final}}-V_{\text{initial}})\cdot \exp \left(-\frac{t-t_0}{\tau }\right)\end{array}$$

Example Problem 1:

Example Problem 2: