Step 1 :Given that the initial amount of the substance \(N_0 = 7\) grams, the time that has passed \(t = 4\) minutes, and the half-life of the substance \(h = 5.76\) minutes.
Step 2 :We can calculate the final amount of the substance \(N\) using the formula \(N = N_0 \times (1/2)^{t/h}\).
Step 3 :Substituting the given values into the formula, we get \(N = 7 \times (1/2)^{4/5.76}\).
Step 4 :Rounding to three decimal places, we find that the final amount of the substance \(N\) is approximately 4.326 grams.
Step 5 :\(\boxed{4.326}\) grams of a 7 gram sample of titanium-51 would remain after 4 minutes.