The bones of a newly discovered dinosaur weigh 170 pounds and measure 9 feet, with a 6-inch claw on one toe of each hind foot. The age of the dinosaur was estimated using a radioactive substance dating of rocks surrounding the bones. Complete parts a and b a. The radioactive substance decays exponentially with a half-life of approximately 1.33 billion years. Use the fact that after 1.33 billion years a given amount of the radioactive substance will have decayed to half the original amount to show that the decay model for the radioactive substance is given by A = Ape 0.52116, where t is in billions of years. To show that the decay model for the radioactive substance is A = Ape 0.521161, find the decay rate k for a substance. Substitute the values of A and t in the exponential decay model, A = Age A = Apekt = Age 1.33k Substitute = 1.33k Divide both sides of the equation by Ao V = Take the natural logarithm on both sides and simplify. =K Solve for K. (Round to five decimal places as needed.) b. Analysis of the rocks surrounding the dinosaur bones indicated that 94.2% of the original amount of radioactive substance was still present. Let A = 0.942A, in the model in part (a) and estimate the age of the bones of the dinosaur The estimated age of these dinosaur bones is about billion years (Round to four decimal places as needed )