Here is the question:

An unknown radioactive element decays into non-radioactive substances. In

days the radioactivity of a sample decreases by

percent.

(a) What is the half-life of the element?

(b)How long will it take for a sample of

mg to decay to

mg?

I've tried it several times and I keep getting the same answers which are wrong

I used $\displaystyle dy/dx=-ky$ I integrate this and got $\displaystyle y=ce^{-kt}$.

I used $\displaystyle y(0)=y_0$ which gave me the equation $\displaystyle y=y_0e^{-kt}$.

I then plugged in $\displaystyle 0.37y_0$ for y and 400 for t from the question. this gave me k= 0.0025. giving me the equation $\displaystyle y(t)=y_0e^{-.0025t}$.

I then set $\displaystyle y(t)= 0.5y_0$ and solved for t to get the half life. Which gave me the answer 277 days.

What am I doing wrong?