Answer:
For the substance to decay to one-half of its original amount, it will take:
10.6 weeks.
Step-by-step explanation:
The decay rate = dQ/dt= -rQ
Where r > 0.
100 mg of a mystery substance decays to 81.14 mg in 4 weeks
This implies that it has decayed by 18.86 mg (100 - 81.14) in 4 weeks
The rate of decay per week = 4.715 mg (18.86 mg/4)
For the substance to decay to one-half of its original amount, i.e. 50 mg (100 mg/2), it will take 10.6 (4/18.86 * 50) weeks.
We can also determine the time it will take the substance to decay by working with the decay rate and the volume of decay, thus:
Decay rate = 4.715 / week
Decay volume = 50 mg (100 mg/2)
Time for 50 mg to decay = Decay volume/Decay rate
= 50 mg/4.715
= 10.6 weeks
