N=NOe^-kt N=mass at time t NO = initial mass k= 0.1476 t= time, in days
We are asked to find the half-life, which means you want to find how long it will take for half of the substance to decay/disappear (depending on situation).
If we are looking for half-life, we can simply set N to half of NO (which we are given a value of 40grams for) Therefore: N = 20 NO = 40 plugging these values and the value given for k back into the equation you get:
20 = 40e^-0.1476(t) We are looking for t, so we have to manipulate the formula to get t by itself on one side of the equation. We can start by dividing 40 from both sides, and you get: 0.5 = e^-0.1476(t)
We have the exponential function "e". To get rid of e, we can use natural log (ln) if e^y=x then ln (x) = y look back at our equation we can set 0.5 = x -0.1476(t) = y
Rewriting it in natural log form: ln (0.5) = -0.1476(t) Plug in ln (0.5) on a calculator to find its value and we get: -0.693147 = -0.1476(t) *Note: normally, getting a negative value would suggest that we did something wrong, because you cannot have a negative value as your t (you cannot have negative days), but because there is a negative on both sides of the equation, they will cancel out in this case.
The last step is to simply divide both sides by -0.1476 therefore: T = 4.696119 But it asks you for the answer to the nearest tenth (one place after decimal pt) so T (half life) = 4.7 days
