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.

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I got to this point and couldn’t figure out where I went wrong:

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

ln (0.5/600) =-0.00383t

t=1851.194996

Somehow, when I submitted that answer it was incorrect. What am I doing wrong?

Answer 1

D(t)=600e^-0.00383t

Don't use .5. Use 300 grams. Because, that's whats left after one half life.

300 = 600e^-0.00383t