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ykpwincess
27.09.2019 •
Mathematics
Aflu has hit a city and the percentage of a population with the flu, t days after the disease arrives is approximated by f(t)=10te^(-t/8) for 0< =t> =40.
1)after how many days is the percentage of the population with the flu a maximum?
2)what is the maximum percent of the population at this time?
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Ответ:
f(t)' = 10(e^(-t/8) + t*e^(-t/8)*(-1/8)) = 10(e^(-t/8) -t/8*e^(-t/8)) = 10e^(-t/8)(1-t/8)
the condition is:
f(t)' = 0 that means:
0 = 10e^(-t/8)(1-t/8)
10t/8*e*(-t/8) = 10*e^(-t/8)
t/8 = 1
t = 8
The answer is 8 days.
2) that percent we will get simply by expressing t=8 in our equation.
f(8) = 10*8*e^(-1) = 80/e = 29.43%
Ответ:
b) 0.3x0.8 = 0.24