Adisease has hit a city. the percentage of the population infected t days after the disease arrives is approximated by p(t)=8t e^-t/11 for 0

After 11 days,

32.37%.

Step-by-step explanation:

We have been given that a percentage of the population infected t days after the disease arrives is approximated by for .

In order to find the days when percentage of infected population is maximum, we will find critical values of the given function by setting its derivative equal to zero.

This is a critical value of the function. It can be the point of minimum or point of maximum. In order to check if it is a point of maximum, we will substitute this value of t in the second derivative (Second Derivative Test).

If we get the sign of second derivative as negative - then we will have a maximum at this value of t.

If we get the sign of second derivative as positive - then we will have a minimum at this value of t.

At , we have second derivative negative as:

Therefore, we do have a maximum at that is after 11 days the percentage of infected people is maximum.

To find the maximum percentage, we need to substitute is the given function.

Therefore, 32.37% is the maximum percent of infected population.

b. the decimal could be two-tenths.

step-by-step explanation: