Question

A substance decays so that the amount A of the substance left after t years is given by:

A = A_0 · (0.9) ^ t ,

where A 0 is the original amount of the substance. What is the half-life (the amount of time that it takes to decay to half the original amount) of this substance rounded to the nearest tenth of a year?

5.6 years
6.1 years
6.6 years
7.5 years

Answer 1

As you can read in the question, the half-life is the time \(\tau\) such that \(A(\tau) = \dfrac{A_0}{2}\).
Can you see how to proceed from here?