Question

a population grows exponentially and doubles in size every 10 years. using P=P0e^kt, where Po represents the population at t=0, find the value of k

Answer 1

here's a shortcut you can learn
\[k = \frac{\ln 2}{t}\]
where t is the time where the population doubles in size so \[k = \frac{\ln 2}{10}\]
does that help?

Answer 2

doubles in ten years so you know
\[2=e^{k\times 10}\] solve for \(k\) yo get
\[\ln(2)=10k\] and so
\[k=\frac{\ln(2)}{10}\] just as written above