Final answer:
Calculating the amount of a substance left when the elapsed time is not a multiple of the half-life requires using the exponential decay equation N(t) = N_0(1/2)^(t/T).
Step-by-step explanation:
When dealing with the decay of radioactive materials or pharmacokinetics in medicine, calculating the survival times or remaining quantity of a substance can be complex. If the elapsed time is not an exact number of half-lives, we use a logarithmic equation to determine the amount left. The decay of a material is described by the equation N(t) = N_0(1/2)^(t/T), where:
- N(t) is the amount of substance that remains after time t.
- N_0 is the original amount of the substance.
- t is the elapsed time.
- T is the half-life of the substance.
As the equation shows, the decay process depends on the half-life, T, which is a fixed period during which half of the original substance decays. To solve for the remaining quantity of a substance when t is not a multiple of T, we input the actual elapsed time into this exponential equation.