A 22 gram sample of a substance thats used to treat thyroid

A 22 gram sample of a substance that\'s used to treat thyroid disorder has a k^- value of 0.138. N = N_0e^-kt N_0 = initial mass (at timed t = 0) N = mass at time t k = a positive constant that depends on the substance itself and on the units used to measure time t = time, in days Find the substance\'s half - life, in days. Round your answer to the nearest tenth. Enter the correct answer

Solution

Half-life of a substance is the time required for exactly half of the quantity to decay. We are given that    N = N₀ e^-kt where N₀ = 22gms, k = 0.138 and t is the number of days. We have to find t when N = 11gms. On substituting these values in the given equation, we have 11 = 22e^-0.138t, or, e^-0.138t = 11/22 = ½. = 0.50. On taking natural logarithms of both the sides, we have ln (0.50) = -0.138t ( as ln e = 1) or, -0.138t = - 0.69314718. Therefore,    t = 0.69314718 / 0.138 = 5.02 days = 5 days on rounding off to the nearest whole number.