A half-life is the amount of time that it takes for a radioactive subs

1.	A half-life is the amount of time that it takes for a radioactive substance to decay one-half of its original quantity.Suppose radioactive decay causes 300 grams of a substance to decrease 300 x 2-3 grams after 3 half-lives. Evaluate 300 x 2-3 to determine how many grams of the substance is left.Explain why the expression 300 x 2-n can be used to find the amount of the substance that remains after n half-lives.
Answer» Given, 300 grams of a substance decrease to 300 × 2^-3 after 3 half-lives. ⇒ Evaluating 300 × 2^-3 We know by laws of exponents, a^-n = 1/aⁿ ⇒ 300 × 2^-3 = 300 x 1/2² = 300 x 1/8 = 75/2 = 37.5 grams ∴ 3.75 grams of the substance are left.

A half-life is the amount of time that it takes for a radioactive substance to decay one-half of its original quantity.Suppose radioactive decay causes 300 grams of a substance to decrease 300 x 2-3 grams after 3 half-lives. Evaluate 300 x 2-3 to determine how many grams of the substance is left.Explain why the expression 300 x 2-n can be used to find the amount of the substance that remains after n half-lives.

Answer»

Given, 300 grams of a substance decrease to 300 × 2^-3 after 3 half-lives.

⇒ Evaluating 300 × 2^-3

We know by laws of exponents, a^-n = 1/aⁿ

⇒ 300 × 2^-3

= 300 x 1/2²

= 300 x 1/8

= 75/2

= 37.5 grams

∴ 3.75 grams of the substance are left.