To find the half-life of the radioactive substance, we can observe the data given:
- At Day 0, the mass is 100 g.
- At Day 1, the mass is 90 g.
- At Day 2, the mass is 81 g.
- At Day 3, the mass is 73 g.
First, let's find the decay rate over the days:
- From Day 0 to Day 1: Mass decreases from 100 g to 90 g.
- From Day 1 to Day 2: Mass decreases from 90 g to 81 g.
- From Day 2 to Day 3: Mass decreases from 81 g to 73 g.
The rate of decay does not appear to be consistent, indicating that we cannot find an integer based on simple subtraction. Instead, we can calculate the half-life directly.
The half-life is the time it takes for the mass of the substance to reduce to half of its original amount.
Starting with 100 g:
- Half of 100 g is 50 g.
- There is no day recorded in which the mass is exactly 50 g. However, we can check when it decreases significantly:
Given the trend in this data, it appears that the mass decreases by a rate of approximately 10 g, 9 g, and then 8 g over each specific day.
Approximate decay process:
- 100 g -> 90 g (Day 1)
- 90 g -> 81 g (Day 2)
- Approximate next prediction would lead to further gradual decline as it does not seem linear.
Since there isn't a clear pattern here showing a clean half-life, we can notice that this isn't strictly half-life decay.
Another approach is to integrate the exponential decay function if needed for more significant calculation estimates.
Since we don't reach exactly half within 3 days:
A better estimate (after analyzing the decay pattern) may be around 10 days, as indicated in the options offered as half-life.
Thus, based on this information and the observed mass changes, the very best guess as the most appropriate estimation based on decay patterns perhaps observes half-lives similar to those close to other decay processes previously studied.
Therefore, based on the provided answers and assumptions we have:
The half-life of the radioactive substance is likely 10 days.