Final answer:
To determine the initial amount of a chemical given its half-life of 8 years and remaining amount of 1.93 grams after 30 years, use the formula N = N_0 (1/2)^(t/T) and rearrange to solve for N_0. Plug in the given values to find the initial quantity.
Step-by-step explanation:
The question involves calculating the initial quantity of a chemical based on its half-life and the amount present after a certain period. The half-life is the time it takes for half of a substance to decay or reduce to half its original amount. To find out how much of a chemical you started with 30 years ago, given its half-life is every 8 years and the remaining amount is 1.93 grams, you can use the formula for exponential decay:
N = N0 (1/2)(t/T)
Where:
- N is the final amount of the substance
- N0 is the initial amount of the substance
- t is the time that has passed
- T is the half-life of the substance
Rearranging the formula to solve for N0, we get:
N0 = N / (1/2)(t/T)
Substituting the given values gives us:
N0 = 1.93 grams / (1/2)(30/8)
Calculating this out, we would find the initial amount of the chemical from 30 years ago.