Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Explore thousands of questions and answers from a knowledgeable community of experts ready to help you find solutions. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
so, the car depreciates by half every 5 years, or namely it depreciates by 50% every 5 years, so
[tex]\textit{Periodic/Cyclical Exponential Decay} \\\\ A=P(1 - r)^{\frac{t}{c}}\qquad \begin{cases} A=\textit{current amount}\dotfill &\$7000\\ P=\textit{initial amount}\dotfill &\$19000\\ r=rate\to 50\%\to \frac{50}{100}\dotfill &0.5\\ t=\textit{elapsed time}\\ c=period\dotfill &5 \end{cases}[/tex]
[tex]7000=19000(1-0.5)^{\frac{t}{5}}\implies \cfrac{7000}{19000}=0.5^{\frac{t}{5}}\implies \cfrac{7}{19}=0.5^{\frac{t}{5}} \\\\\\ \log\left( \cfrac{7}{19} \right)=\log\left( 0.5^{\frac{t}{5}} \right)\implies \log\left( \cfrac{7}{19} \right)=t\log\left( 0.5^{\frac{1}{5}} \right) \\\\\\ \log\left( \cfrac{7}{19} \right)=t\log( \sqrt[5]{0.5})\implies \cfrac{\log\left( \frac{7}{19} \right)}{\log( \sqrt[5]{0.5})}=t\implies 7.2\approx t[/tex]
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.