Final answer:
The half-life formula for a radioactive isotope is amount remaining = (amount initial) × e^(-t/t1/2), where e is the base of natural logarithms, t is the elapsed time, and t1/2 is the half-life of the isotope. The variables t and t1/2 must have the same units of time. The formula can be used to calculate how much of a radioactive isotope remains after a certain amount of time.
Step-by-step explanation:
The half-life formula for a radioactive isotope is given by:
amount remaining = (amount initial) × e^(-t/t1/2)
Here, e is the base of natural logarithms (approximately 2.71828182), t is the elapsed time, and t1/2 is the half-life of the isotope. The variables t and t1/2 must have the same units of time. To evaluate the exponential function, you may need to use a calculator or an inverse logarithm function. It is important to note that the length of time t does not need to be an exact multiple of half-lives.