If a radioactive substance has a half-life of $10$ days, in how many days will $1/8$ of the initial amount be present? Assume the decaying process is continuous (exponential).
Will the answer just be $30$ days, or is it different if it is continuous?
The half-life indicates exactly when the substance will be halved. In this case $1/8$ is a power of $1/2$, so there is no difference between a discrete and a continuous process.
Things would be different if you would need to find, say, in how many days the substance will reach $1/36$ of the initial amount.
