Mathematics
uhfinn:

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

DuarteME:

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?