This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Write down the given formula and substitute the known values. The formula for radioactive decay is A(t) = A_0e^-kt. We are given that after two hours (t=2), 0.9 A_0 remains, so A(2) = 0.9 A_0. Substitute these values into the formula: 0.9 A_0 = A_0e^-k(2) Step 2: Simplify the equation by dividing both sides by A_0. 0.9 = e^-2k Step 3: Take the natural logarithm () of both sides to solve for k. (0.9) = (e^-2k) Using the logarithm property (e^x) = x: (0.9) = -2k Step 4: Isolate k. k = ((0.9))/(-2) k = -((0.9))/(2) Step 5: Calculate the numerical value and round to 2 decimal places. k ≈ -(-0.1053605)/(2) k ≈ 0.05268025 Rounding to two decimal places: k ≈ 0.05 The value of k is: k = 0.05 Last free one today — make it count tomorrow, or type /upgrade for unlimited.