Exponential growth and decay (probability and statistics)

Question

I really need help solving this problem for my probability and statistics class. I need to show the algebra I used to achieve my results.

The mass of a radioactive substance remaining after t years is given by:

M=1000Xe^-0.05t

   Find the exact time when the mass will reach half its original value.

Answer 1

So when the mass is 1/2 the original value you have the equation

500= 1000e^-.05t

e^-.05t = 500/1000

e^-.05t=.5. Now take the natural log of both sides of the equation

-.05t=ln.5

t= ln.5/-.05= 13.863yrs rounded to the nearest thousand