Problem
Question A radioactive substance has a continuous decay rate of 0.056 per minute. How many grams of a 120 gram sample will remain radioactive after 40 minutes? Round the answer to the nearest tenth of a gram, and do not include the unit in your answer. Sorry, that's incorrect. Try again? \[ 12.0 \] FEEDBACK VIEW ANSWER SUBMIT Content attribution
Solution
Step 1 ：Given that the initial amount of the substance, \(N_0\), is 120 grams, the decay constant, \(\lambda\), is 0.056 per minute, and the time, \(t\), is 40 minutes.
Step 2 ：The decay of a radioactive substance can be modeled by the exponential decay formula: \(N = N_0 * e^{-\lambda t}\), where \(N\) is the final amount of the substance.
Step 3 ：Substitute the given values into the formula: \(N = 120 * e^{-0.056*40}\).
Step 4 ：Calculate the above expression to find the final amount of the substance, \(N\).
Step 5 ：\(\boxed{N \approx 12.0 \text{ grams}}\). So, approximately 12.0 grams of the radioactive substance will remain after 40 minutes.
