Answer:
6.575 trillion BTUs
Step-by-step explanation:
<em>Let represent the annual energy consumption of the town as E</em>
<em>The rate of annual energy consumption * energy consumption at time past</em>
<em>dE/dt * E</em>
<em>dE/dt =K</em>
<em>k = the proportionality constant</em>
<em>c= the integration constant</em>
<em>(dE/dt=) kdt</em>
<em>lnE = kt + c</em>
<em>E(t) = e^kt+c ⇒ e^c e^kt e^c is a constant, and e^c = E₀</em>
<em>E(t) = E₀ e^kt</em>
<em>The initial consumption of energy is E(0)=4.4TBTU</em>
<em>set t = 0 then</em>
<em>4.4 = E₀ e⇒ E₀ (1) </em>
<em>E₀ = 4.4</em>
<em>E (t) = 4.4e^kt</em>
<em>The consumption after 5 years is t = 5, e(5) = 5.5TBTU</em>
<em>so,</em>
<em>E(5) = 5.5 = 4.4e^k(5)</em>
<em>e^5k = 5/4</em>
<em>We now take the log 5kln = ln(5/4)</em>
<em>5k(1) = ln(5/4)</em>
<em>k = 1/5 ln(5/4) = 0.04463</em>
<em>We find the town's annual energy consumption, after 9 years</em>
<em>we set t=9 </em>
<em>E(9) = 4.4e^0.04463(9)</em>
<em>= 4.4(1.494301) = 6.5749TBTUs</em>
<em>Therefore the annual energy consumption of the town after 9 years is </em>
<em>= 6.575 trillion BTUs</em>
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