Question

How do you convert P=P(sub)0*a^t to P(sub)0*e^kt and vice versa?

What's the difference?

Answer 1

\[
P(t)=P_0\cdot a^t\to P_0e^{kt}
\]

Answer 2

Start with: \[
a^t=e^{kt}
\]

Answer 3

Solve for \(k\). This means you want to do logarithms. \[\begin{split}
\ln(a^t)&=\ln(e^{kt})\\
t\ln(a)&=kt\\
\ln(a)&=k
\end{split}\]

Answer 4

Basically\[
P(t)=P_0\cdot a^t =P_0e^{\ln(a)t}
\]

Answer 5

Thanks so much!