The rate at which people learn about a secret is directly proportional to the number of people who know the secret. If two people know the secret on day 0, and 20 people know it on day 2, how long will it take for the whole school (4000 people) to know?

Answer 1

dy/dx = ky
dy/y = k dx
lny = kx + lnc
y(x) = c*e^(kx)
Now use
y(0) = 2
y(2) = 20
to find c and k
Then solve for x when y=4000

Answer 2

or, use the points to discover that y = 2*10^(x/2)