Question

A disease has hit a city. The percentage of the population infected t days after the disease arrives is approximated by ​p(t)equals8 t e Superscript negative t divided by 11 for 0less than or equalstless than or equals44. After how many days is the percentage of infected people a​ maximum? What is the maximum percent of the population​ infected?

A. The percentage of infected people reaches a maximum after__ days.


B. The maximum percent of the population infected is __%.

Answer 1

A 11 days

B. 32.37%

Explanation:

`p(t) = 8te^(-t/11)`

percentage of infected people a maximum when p '(t) = 0

==>
`p '(t) = 8(1)e^(-t/11) +8te^(-t/11)(-1/11)`

==>

==> p(11) = 88/e = 25.752 %

=32.37%