Answer:
t = 1180 years
Step-by-step explanation:
We will solve this using the radioactive decay formula which is;
A = A_o × 2^(-t/h)
Where;
A = Amount of liquid remaining after time (t)
A_o = initial amount of liquid at initial time
t = time of decay
h = half-life of the liquid
We have;
A_o = 1(we assume it is 100% which is 1)
A = 0.02% = 0.0002
h = 96 years
Thus;
0.0002 = 1 × 2^(-t/96)
0.0002 = 2^(-t/96)
(-t/96)log 2 = log 0.0002
(-t/96) = (log 0.0002)/log 2
(-t/96) = -12.2877
t = 96 × 12.2877 (negative has canceled out)
t = 1179.6192
To the nearest year gives;
t = 1180 years
