a certain type of radioactive iodine has a halflife of 30 da

a certain type of radioactive iodine has a half-life of 30 days. find an exponential decay model, A=A0e^(kt), for this type of iodine. round the k value in you formula to six decimal places.

Solution

A certain type of radioactive iodine has a half-life of 30 days. The exponential decay model for this type of iodine is A = A₀e^kt where A₀ is the initial quantity, A is the quantity after t days and k is a constant. Hete, when t = 30, A = (1/2) A₀ so that ( 1/2)A₀ = A₀ e^30k or, e^30k = 1/2. On taking natural logarithms of both the sides, we have 30k( ln e ) = ln (1/2) or, 30k = - 0.69314718 ( as ln e = 1). Therefor k =  - 0.69314718 / 30 = -0.023104906 = -0.023105 ( on rounding off to 6 decimal places)