Final answer:
To calculate the time it takes for a substance to decompose to 0.75% of its original amount, knowledge of the half-life is required, and the time can be calculated using the given radioactive decay formula with the actual half-life value.
Step-by-step explanation:
To determine how many days it will take for a sample to decompose to 0.75% of its original amount, we need to know the half-life of the substance in question. The decay of radioactive elements is exponential, and each half-life reduces the remaining quantity by half. Using the half-life of a substance, the time to decay can be calculated using the formula N = N0(1/2)(t/half-life), where N is the final amount, N0 is the original amount, t is the time in units compatible with the half-life, and half-life is the half-life of the substance.
As the question does not provide the half-life, a generalized example can be given with a placeholder half-life value. Suppose a substance has a half-life of x years, to decay to 0.75% of its original amount, we set up the equation 0.0075 = (1/2)(t/x). Solving for t, we get t = x * log2(0.0075). Once the half-life is known, simply plug it in and solve for t to find the number of days.