Question

Salt (NaCl) decomposes in water into sodium (Na+) and chloride (Cl -) ions according to the law of uninhibited decay. If the initial amount of salt is 25 kilograms and, after 15 hours, 15 kilograms of salt is left, how much salt is left after 1 day?

would it be
salt left = 25 - t^x

Answer 1

The general equation is
B = Ae^(-Ct)

at t = 0, A = 25 kg
at t = 10 hrs, B = 15 kg

15 = 25e^(-10C)
e^(-10C) = 15/25
-10C*ln(e) = ln(0.6)
C = -ln(0.6)/10
C = 0.0511

The equation is
B = 25e^(-0.0511t)

Solving for B at t = 24 hrs
B = 25e^(-0.0511*24)
B = 7.34 kg

Solve for t:
B = 25e^(-0.0511t)
e^(-0.0511t) = B/25
-0.0511t = ln(B/25)
t = -ln(B/25)/0.0511
when B = 1/2 kg
t = -ln(0.5/25)/0.0511
t = 76.58 hrs