Recall that your hypothesis is that these values are the fraction of atoms that are still radioactive after n half-life cycles.

Answer: A= 0.5, B = 0.25, C = 0.125, D = 0.015625 and E = 0.00390625

Explanation:

The half-life of a substance refers to the duration it takes for that substance to decrease to half of its original quantity.

Here, n signifies the count of half-lives.

The remaining quantity of the substance after n half-lives can be determined using the formula provided,

When n = 1,

Fraction of substance remaining = 0.5¹ = 0.5.

This indicates that after the first half-life, the remaining quantity is half of the original amount.

Thus, we find A = 0.5

Thus, D = 0.015625

The calculated values for A, B, C, D, and E are 0.5, 0.25, 0.125, 0.015625, and 0.00390625 respectively.