Since the rate of growth is equal to dm/dt, (where m is the mass of the mold), then we get the differential equation

dm/dt = km,

where k is the constant of proportionality. Separating the variables gives the equation

dm/m = kdt.

Integrating both sides gives

ln m = kt + C

Changing to exponential form gives

m = e^{kt + C}

which is equivalent to

m = C₁e^kt

Since m = 3 when t = 0, C₁ = 3.

Substituting m = 5 when t = 2 gives the following:

5 = 3e^2k

Solving this gives (ln(5/3))/2 = k, or

k = .2554128. . .

Now, evaluate the equation when t = 12 and get

m = 64.3 grams.