<s>[INST] When a radioactive substance decays, it loses a fixed proportion of its mass over a fixed time period. This means that the mass left in the substance decreases exponentially. Suppose that we start with a certain amount A of the radioactive substance, and that after every half-life of t hours, the amount becomes \(\frac{1}{2}A\). The population of the substance can be modeled by the equation \(Ae^{-kt}\), where k is a constant.

t in hours             A in grams


| 0          | 30         |
| 2          | 15         |
| 4          | 7.5        |
| 6          | 3.75       |
| 8          | 1.875      |

What is the half-life, t, of the given substance?[/INST]