Question

During a certain epidemic, the number of people that are infected at any time increases at rate proportional to the number of people that are infected at that time. 1,000 people are infected when the epidemic is first discovered, and 1,200 are infected 7 days later.

Write and exponential growth model for the epidemic. Let t represent time in days.

I got k=.0260459367 but then what's the fianl equation?

Answer 1

di/dt = k i
di/i = k dt
ln i = kt + c

i = e^(kt+c) = C e^kt

here
200/7 = k (1000)
k = .02875

i = 1000 e^(.02875 t)

Answer 2

or more accurately
i = 1000 e^kt
1200 = 1000 e^7k
e^7k = 1.2
7 k = ln 1.2
k = .0260459367 as you said