Final answer:
Element X decays radioactively with a half-life of 14 minutes. It would take approximately 9.6 minutes for the Element X to decay to 11 grams.
Step-by-step explanation:
The decay of Element X can be modeled by an exponential decay equation: N(t) = N0 * (1/2)(t/half-life), where N(t) is the amount of Element X remaining at time t, N0 is the initial amount of Element X, and the half-life is 14 minutes.
To find the time it takes for Element X to decay to 11 grams, we can solve the equation 11 = 160 * (1/2)(t/14) for t.
By taking the logarithm on both sides of the equation and rearranging, we find that t ≈ 9.6 minutes to the nearest tenth of a minute.