1. The exponential decay formula is A = Pe^(rt), where A is the amount of radioactive isotope, P is the initial amount, r is the decay rate, and t is the time in hours. The half-life of Pu-243 is 5 hours, which means that the decay rate is k = ln(1/2)/5 = -0.13863.
Substituting the given values, we get A = 88e^(-0.13863t). The decay rate is -0.13863 grams/hour (rounded to 5 decimal places).
2. To find how much would be left in 1 day, we can substitute t = 24 into the equation A = 88e^(-0.13863t). A = 88e^(-0.13863*24) = 6.91 grams (rounded to the nearest hundredth).
3. To find how long it would take to end up with 2 grams, we can set A = 2 in the equation A = 88e^(-0.13863t) and solve for t. 2 = 88e^(-0.13863t). Divide both sides by 88 to get e^(-0.13863t) = 0.02273. Take the natural logarithm of both sides to get -0.13863t = ln(0.02273). Divide both sides by -0.13863 to get t = 15.9 hours (rounded to the nearest tenth).