Answer:
Assume the radioactive dye decays exponentially. Let t = time in minutes. The amount present obeys the equation
A(t) = A0e-kt,
k = a positive constant
t = minutes elapsed from the time when A was A0
In milligrams,
4 = 15e-k(20)
k = [-ln(4/15) / 20] min-1 ≅ 0.06609 min-1
Set
2 = 15e-0.06609t
and solve for t.
t = -ln(2/15) / (-0.06609) min ≅ 30.49 min
It takes about 30.49 minutes for 15 milligrams to decay down to 2 milligrams.
Explanation: