During the month of February, a flu epidemic hit the University. The number of people sick at

time t (measured in days) is given by the function P(t). The rate at which the epidemic is
spreading on February 3 is 110 people per day. How is the information best represented mathematically?

my answer is P(3)=110. Is this correct or would it be P'(3)=110?

If time t is measured in days from the beginning of the month, P(3)=110 is correct. Since the datum of t is not mentioned, you will have to specify this in your answer.

P'(3) is usually used to mean the rate of change (increase) of the number of infected per day, i.e. how many more per day.

So if though it says that the rate at which the epidemic is spreading is 110 per day that is not rate of change correct?

Perform the indicated operation

-42+6-(-7)-14 is that correct

To represent the given information mathematically, we need to consider the rate at which the epidemic is spreading. The rate of change of the number of people sick with the flu is represented by the derivative of the function P(t).

Therefore, the correct representation for the rate at which the epidemic is spreading on February 3 would be P'(3) = 110, where P'(t) represents the derivative of the function P(t) with respect to time.

In this case, P(t) represents the number of people sick at time t, and P'(3) represents the rate of change of the number of people sick at time t = 3. So, P'(3) = 110 means that on February 3, the flu epidemic was spreading at a rate of 110 people per day.