A disease 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 8 for 0less than or equalstless than or equals32. After how many days is the percentage of infected people a maximum? What is the maximum percent of the population infected?

(1) The percentage of infected people will be a maximum after 8 days.

(2) The maximum percent of the population infected is 20.60%.

Step-by-step explanation:

The percentage of the population infected t days after the disease arrives is approximated by:

(1)

The percentage of infected people will be a maximum when p' (t) = 0.

Compute the value of p' (t) and equate it to 0 as follows:

Thus, the percentage of infected people will be a maximum after 8 days.

(2)

Compute the value of p (8) as follows:

Thus, the maximum percent of the population infected is 20.60%.