Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Our platform offers a seamless experience for finding reliable answers from a network of experienced professionals. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
we know that initially there were 120 colonies or namely that C = 120, well, what time was that? that was the hour 0, or namely t = 0, so then
[tex]P=Ce^{rt}\qquad \begin{cases} P=\textit{accumulated amount}\\ C=\textit{initial amount}\dotfill &120\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time}\dotfill &0\\ \end{cases} \\\\\\ P=120e^{r\cdot 0}\implies P=120e^0\implies P=120\cdot 1\implies P=120[/tex]
we also know that when t = 4, C = 550
[tex]\textit{Amount of Population Growth} \\\\ P=Ce^{rt}\qquad \begin{cases} P=\textit{accumulated amount}\dotfill&120\\ C=\textit{initial amount}\dotfill &550\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time}\dotfill &4\\ \end{cases} \\\\\\ 120=550e^{4r}\implies \cfrac{120}{550}=e^{4r}\implies \cfrac{12}{55}=e^{4r}~\hfill \stackrel{\textit{using this log cancellation rule}}{\log_a(a^x)=x}[/tex]
[tex]\log_e\left( \frac{12}{55}\right)=\log_e(e^{4r})\implies \log_e\left( \frac{12}{55}\right)=4r\implies \ln\left( \frac{12}{55}\right)=4r \\\\\\ \cfrac{\ln\left( \frac{12}{55}\right)}{4}=r\implies -0.381\approx r = k[/tex]
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.
