160mg of Na^24. There was only 20mg left 45h later. What is the halflife of the Na^24?

Question

this is a math question in calculus and i need to know how to get the answer...step by step if possible...i already know the answer is 15 hours

Answer 1

15 hours
2^-(T/H) = left/original = 20 mg/160mg = 1/8
ln 2^-(T/H) = ln 0.125 = -(T/H) * ln 2 = ln 0.125

T = 45, H = half-life.

H = -T * ln 2/ln 0.125 = 15

Answer 2

Half life is how long it takes to for half of the mass to dissappear.

How many half-life's did it go through?

160 mg --> 80 mg --> 40 mg --> 20 mg

It went through 3 half lifes.

45 hours / 3 = 15 hours