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The following model was estimated for COVID-19 in British Columbia before lockdown was in place: lnY=2.66+.20*t...

  1. The following model was estimated for COVID-19 in British Columbia before lockdown was in place:

lnY=2.66+.20*t

Where Y is total Covid-19 cases and t is time in days since the first occurrence. In how many days will cases double if this pattern persists? (Provide a number)

math   Statistics-And-Probability   
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Answer #1

\\ \ln y=2.66+0.2t\\ \Rightarrow y=e^{2.66+0.2t}\ \ \ \ \\ \\ At\ initial\ time\ t\\ y=e^{2.66+0.2t}\ \ \ \ \ \dots (i)\\ \\ Let\ after\ x \ year\ the\ population\ is\ double\\ So,\ 2y=e^{2.66+0.2(t+x)}\dots(ii)\\ \\ operating\ (i)/(ii) we\ get\\ \\ \frac{2y}{y}=\frac{e^{2.66+0.2(t+x)}}{e^{2.66+0.2t}}\\\\ \Rightarrow 2=e^{2.66+0.2t+0.2x-2.66-0.2t}\\ \Rightarrow 2=e^{0.2x}\\ \Rightarrow \ln 2=\ln e^{0.2x}\\ \Rightarrow \ln 2=0.2x\\ \Rightarrow x=5\ln 2=3.4657

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