Question

A scientist begins with 40 grams of radioactive substance. After 6 days the sample has decayed to 28 grams. Find the half life of this substance. Clearly show the process in answering this question.

Answer 1

Using the exponential decay formula, the half-life of a radioactive substance that decayed from 40 grams to 28 grams in 6 days is calculated to be approximately 9.97 days.

Step-by-step explanation:

The student is asking to find the half-life of a radioactive material, which requires using exponential decay principles in mathematics. The problem states that 40 grams of a radioactive substance decays to 28 grams in 6 days. To find the half-life, we need to use the formula for exponential decay:

N = N_0 (1/2)^(t/T)

where N is the final amount, N_0 is the initial amount, t is the time that has passed, and T is the half-life.

Substituting the values we have:

28 = 40 (1/2)^(6/T)

Solving for T gives:

0.7 = (1/2)^(6/T)

Now, converting to logarithmic form to solve for T:

log(0.7) = (6/T) log(0.5)

T = 6 / (log(0.7) / log(0.5))

Using a calculator to find T gives approximately:

T ≈ 9.97 days

Therefore, the half-life of the substance is approximately 9.97 days.