Mathematics, 04.07.2019 01:00 zahrast14
Adisease has hit a city. the percentage of the population infected t days after the disease arrives is approximated by p(t)equals7 t e superscript negative t divided by 12 for 0less than or equalstless than or equals48. after how many days is the percentage of infected people a maximum? what is the maximum percent of the population infected? the percentage of infected people reaches a maximum after how many days.
Answers: 1
![\Rightarrow P'(t)=\frac{d}{dt}[7te^{-\frac{t}{12}}]=7[t.\frac{d}{dt}(e^{-\frac{t}{12}})+\frac{d}{dt}(t).e^{-\frac{t}{12}}]\\\\\Rightarrow P'(t)=7[t.(-\frac{1}{12}\times e^{-\frac{t}{12}})+1.e^{-\frac{t}{12}}]\\\\\Rightarrow P'(t)=7[e^{-\frac{t}{12}}-\frac{t}{12}e^{-\frac{t}{12}}}]\\\\\Rightarrow P'(t)=7e^{-\frac{t}{12}}[1-\frac{t}{12}}]](/tpl/images/0048/3478/45687.png)
![\Rightarrow 7e^{-\frac{t}{12}}[1-\frac{t}{12}}]=0](/tpl/images/0048/3478/b1795.png)
![\Rightarrow [1-\frac{t}{12}}]=0](/tpl/images/0048/3478/fefcb.png)
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Adisease has hit a city. the percentage of the population infected t days after the disease arrives...
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