Answered

Discover answers to your questions with Westonci.ca, the leading Q&A platform that connects you with knowledgeable experts. Our platform connects you with professionals ready to provide precise answers to all your questions in various areas of expertise. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

How long will it be (hours) until a silo filled with 50 tons of grain is half empty if the silo is emptying at the rate of 4% per hour

Sagot :

[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill &\stackrel{half~empty}{25~\hfill }\\ P=\textit{initial amount}\dotfill &50\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=\textit{elapsed time}\\ \end{cases}[/tex]

[tex]25=50(1-0.04)^t\implies \cfrac{25}{50}=(1-0.04)^t\implies \cfrac{1}{2}=0.96^t \\\\\\ \log\left( \cfrac{1}{2} \right)=\log(0.96^t)\implies \log\left( \cfrac{1}{2} \right)=t\log(0.96) \\\\\\ \cfrac{\log\left( \frac{1}{2} \right)}{\log(0.96)}=t\implies 16.9797\approx t\implies \stackrel{hr}{17}\approx t[/tex]

We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.