The mass of a radioactive substance follows a continuous exponential decay model, Q(t) = Q₀e^rt, with variables Q for quantity and t for time, and constants Q₀ for initial quantity and r for decay rate. Use the tables to help answer the related problems below. Do not round your answers.

a 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

e^a 0.82 0.67 0.55 0.45 0.37 0.30 0.25 0.20

b 1/2 1/3 1/4 1/5 1/6 1/7 1/8 1/9

ln(b) 0.69 1.10 1.39 1.61 1.79 1.95 2.08 2.20

(a) One particular radioactive substance has a decay rate of 10% per day.

i. Find the half-life of this substance (that is,the time it takes for one-half the original amount in a given sample of this substance to decay).

ii. A scientist has a 300-gram sample of this radioactive substance. Find the mass of the sample after 16 days.

(b) Another radioactive substance has a decay rate of 20% per hour.

i. Find the time for this substance to reduce to one-third of its original mass

ii. Our scientist receives a sample,and measures its mass six hours later. If her measurement is 900 grams, what was the original mass when the sample was received?