Answer:
5.33
Explanation:
The amount of a substance decaying exponentially with a half-life can be modeled using the formula A = A₀ * 2^(-t / h), where A is the amount remaining after time t, A₀ is the initial amount of substance, t is the time elapsed, and h is the half-life of the substance. Using the fact that initially there were 12 grams of the substance, and after 2 hours there were 7 grams, we can solve for the half-life h. Substituting the values into the equation 7 = 12 * 2^(-2 / h) and solving, we get that h is approximately 4.145 hours. Finally, we can use the formula A = A₀ * 2^(-t / h) to find the amount of substance remaining after 3 hours. Plugging in A₀ = 12, t = 3, and h ≈ 4.145, we get A ≈ 5.33 grams. Rounding to the nearest hundredth, we conclude that approximately 5.33 grams of the substance will remain after 3 hours.