Utilizing Mathematica, please help me develop an algorithm to solve Problem 2.

Background information-Problem 1:

2. A drug administered to a patient produces a concentration in the blood- stream given by c(t) = Ate-t/3 milligrams per milliliter, t hours after A units have been injected. The maximum safe concentration is 1mg/mL. Use your algorithm developed in problem lb to determine when the concentration of drug reaches a maximum in the blood stream. What amount of the drug should be injected to reach the maximum safe concentration? 1. Plot the function f(x) = 23 cos(x). (a) Use Find Root to locate a root near x = 3 (b) Write a program in Mathematica implementing Newton's method with a while loop instead of a For loop. Use your program to approximate the root near x = -1. Set the maximal number of iterations to 100 and the kick out threshold or tolerance, to 10-4. Display in a table the iteration number, the approximate root, the residual, \f (xn) and successive iteration errors, Xn Xn-1) at each iteration. How many iterations does your program actually execute before it stops? Using the result of (a) as the actual and this result as the computed, calculate the relative absolute error (same as relative error as defined in class) 2. A drug administered to a patient produces a concentration in the blood- stream given by c(t) = Ate-t/3 milligrams per milliliter, t hours after A units have been injected. The maximum safe concentration is 1mg/mL. Use your algorithm developed in problem lb to determine when the concentration of drug reaches a maximum in the blood stream. What amount of the drug should be injected to reach the maximum safe concentration? 1. Plot the function f(x) = 23 cos(x). (a) Use Find Root to locate a root near x = 3 (b) Write a program in Mathematica implementing Newton's method with a while loop instead of a For loop. Use your program to approximate the root near x = -1. Set the maximal number of iterations to 100 and the kick out threshold or tolerance, to 10-4. Display in a table the iteration number, the approximate root, the residual, \f (xn) and successive iteration errors, Xn Xn-1) at each iteration. How many iterations does your program actually execute before it stops? Using the result of (a) as the actual and this result as the computed, calculate the relative absolute error (same as relative error as defined in class)