A disease has hit a city. The percentage of the population infected t days after the disease arrives is approximated by p(t)=12t e^-t/7 for 0 less than or equal t less than or equal 42. After how many days is the percentage of infected people a maximum? What is the maximum percent of the population infected?

Question

A disease has hit a city. The percentage of the population infected t days after the disease arrives is approximated by p(t)=12t e^-t/7 for 0 less than or equal t less than or equal 42. After how many days is the percentage of infected people a maximum?  What is the maximum percent of the population infected?

mathstudent55 · Answer

Take the derivative of the equation and set it equal to zero.
Then solve for t to find a maximum value.