Question

A scientist begins with 100 milligrams of a radioactive substances that decays exponentially at a rate of 2.5% every hour. How many milligrams will remain after 54 hours? Round your answer to two decimal places

Answer 1

To find the amount of radioactive substance remaining after a given time, we can use the formula: Amount remaining = Initial amount * (1 - decay rate)^number of hours. In this case, the initial amount is 100 milligrams and the decay rate is 2.5%. Using this formula, we can calculate that the amount remaining after 54 hours is approximately 18.97 milligrams.

Step-by-step explanation:

To find the amount of radioactive substance remaining after a given time, we can use the formula:

Amount remaining = Initial amount * (1 - decay rate)^number of hours

In this case, the initial amount is 100 milligrams and the decay rate is 2.5% (or 0.025). So, the formula becomes:

Amount remaining = 100 * (1 - 0.025)^54

Using a calculator, we can calculate that the amount remaining after 54 hours is approximately 18.97 milligrams.