An influenza epidemic has an infection rate modeled by I ' (t)=30 e0.04 t , where t is time

Question

measured in days since the start of the epidemic on January 14th , and I '(t) measures the infection rate
in people per day. On January 14th there were 800 infected people on record.

a) Fully determine the function I (t), describing the total number of people infected on day t.
Remember to determine the constant c.

b) How many people became infected, to the nearest whole person, between January 14
and January 17th , that is, on the t-interval [0,3] ?

Answer 1

I am sure you meant

I ' (t) = 30 e^(.04t)

then I = 750 e^(.04t) + c
when t=0 , (Jan 14), I = 800
800 = 750 e^(0) + c
50 = c

a) I(t) = 750 e^(.04t) + 50

b) evaluate I(3) and I(0), then subtract the results.