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The decay of 934 mg of a radioactive substance is given by A(t) = 934e^-0.015t, where t is time in years. Find the amount left after 67 years.

A. 171 mg
B. 342 mg
C. 920 mg
D. 337 mg

1 Answer

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Final answer:

To calculate the amount of a radioactive substance left after 67 years, the time is substituted into the decay function, yielding approximately 342 mg.

Step-by-step explanation:

The decay of a radioactive substance is mathematically represented by an exponential decay function. In the given problem, the initial amount of the substance is 934 mg and the decay function is A(t) = 934e^-0.015t, where t is the time in years. To find the amount left after 67 years, we replace t with 67 in the decay function and calculate A(67).

A(67) = 934e^(-0.015 × 67) = 934e^(-1.005) ≈ 934 × 0.3657 ≈ 341.5358 mg

The closest answer to our calculation is 342 mg, so the correct answer is B. 342 mg.

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