Question 10, 5 HW Score: 81.76%, 8.18 of 10 points Part1 of5 Points: 0 of 1 Homework: Section 5.1 p1 A person is given an injection of 500 milligrams of penicillin at time t = 0. Let f(t) be the amount (in milligrams) of penicillin present in the person's bloodstream t hours after the injection. Then, the amount of penicillin decays exponentially, and a typical formula is f(t)= 500 e _ om. Complete parts (a) through (0) below. (a) Give he differential equation satised by f(t). Ht} = A sample of 15 grams of radioactive material is placed in a vault. Let P(t) be the amount remaining after t years, and let Pm satisfy the differential equation P'(t) = U.036P(t). Answer parts (a) through (9). (a) Find the formula for P(t). P(t)= 152 '0')\" (Type an expression using t as the variable.) (b) What is P(0)? P(0) : 15 (c) What is the decay constant? 0.036 (d) How much of the material will remain after 10 years? i V (Type an integer or decimal rounded to one decimal place as needed.) Homework: Section 51 P2