Solve the equation

Question

You have 600-grams of an unknown radioactive substance that has been determined to decay according to:

D(t)=600e^-0.00383t

where t is in years. How long before half of the initial amount has decayed? Set D(t) equal to 1/2 of the starting amount and solve for t.

Answer 1

Use 300 g = 600e^-0.00383t

Answer 2

The problem statement tells you exactly what you need to do to solve the problem.

0.5 = 600 e^-0.00383t

Solve for t using the properties of logarithms.

ln(0.5) = ln(600) - 0.00383t

You should be able to solve for t and finish from here. The value of t will come out in years.