Final answer:
The function that represents the amount of a radioactive substance remaining after time t, given a half-life of 36 hours and an initial amount of 19 grams, is A(t) = 19(1/2)^(t/36).
Step-by-step explanation:
To express the amount of radioactive substance remaining as a function of time t, we need to rely on the concept of half-life. In this case, the half-life of the substance is 36 hours. The formula that links the initial amount with the remaining amount after a certain amount of time is given by: A(t) = A0(1/2)t/T1/2, where A(t) is the amount remaining after time t, A0 is the initial amount, and T1/2 is the half-life of the substance.
Using the data provided in the question, the initial amount of the substance is 19 grams. So the function representing the amount of substance remaining after time t in hours is: A(t) = 19(1/2)t/36.