### Instruction: A radioactive substance decays at a rate proportional to the amount present. If 70% of the substance decays in 20 years, what will be the percentage of the substance left undecayed after 60 years? Answer Choices: (A) 0.9% (B) 2.7% (C) 3% (D) 8.1%.### Response: The decay of a radioactive substance can be modeled by the exponential decay law: N(t) = N0e^(-kt) where N(t) is the amount of the substance at time t, N0 is the initial amount of the substance, k is the decay constant, and e is the base of the natural logarithm. We are given that 70% of the substance decays in 20 years, which means that 30% of the substance remains. This gives us the equation: 0.3N0 = N0e^(-20k) Solving for k, we get: k = -ln(0.3)/20 We are asked to find the percentage of the substance left undecayed after 60 years. This gives us the equation: N(60) = N0e^(-60k) Substituting the value of k that we found, we get: N(60) = N0e^(-60 * -ln(0.3)/20) = N0 * (0.3)^3 = 0.027N0 So, 2.7% of the substance will be left undecayed after 60 years. The answer is B.