Answer:
The amount of a radioactive substance remaining after a certain period of time can be calculated using the formula for exponential decay, which is based on the half-life of the substance. The formula is:
A = A0 * (1/2)^(t/T)
where:
- A is the amount of the substance remaining after time t,
- A0 is the initial amount of the substance,
- t is the time that has passed, and
- T is the half-life of the substance.
In this case, we are given that A0 (the initial amount of iodine-131) is 200 grams, and T (the half-life of iodine-131) is 8 days. We want to find an expression for A, the amount of iodine-131 remaining after t days.
Substituting these values into the formula gives us:
A = 200 * (1/2)^(t/8)
This equation tells us that to find the amount of iodine-131 remaining after t days, we multiply 200 by one-half raised to the power of t divided by 8.