Can you please help? Q3 Exponential Model from a Table of DataTechnetium-99m is a drug taken by a patient and then used to study tumors in the brain, lungsand other parts of the body. The data below shows how much active ingredient, in miiligrams,remains in the body over 6-hour time intervals.Technetium-99m DecayAmount of Drug# of 6-hour timeintervalsremaining (mg)100015002503.125Q3.1 Part a)What is the initial amount of drug the patient took? Include units.Enter your answer hereSave AnswerQ3.2 Part b)Assume that the above data exhibits an exponential behavior. Determine an exponentialequation in the form y = Cb* that models the behavior of Technetium-99m in thebloodstream as a function of time intervals of 6 hours. Show all work. Define all variables.Upload a PDF file of your work. Make sure your PDF file is in the correct orientationO Please select file(s)Select file(s)Save AnswerQ3.3 Part c)What is the decay rate? Provide your answer in context of the problem as a percentage. Usecomplete sentence(s).Enter your answer here

Given that Technetium-99 is a drug taken by the patient an then used to study tumors in the brain ,lungs and other parts of body.The given table gives how much active ingredient in milligrams remains in the body over 6-hour time intervals. It is known that the exponential function has the for y=abx,where a is the y-intercept and b is the base or multiplying factor.Also it is called the growth or decay factor.If b>1 b will be a growth factor and if 0<b<1 b will be a decay factor. a) It is required to given the initial amount of drug taken by the patient. From the given table it is observed that at time t=0 the amount of drug remaining is 1000. Therefore, the initial amount of drug taken by the patient is 1000mg. b) It is required to find the exponential function y=Cbx that models the behavior of technetium-99m in the bloodstream as function of time intervals of 6 hours. First substitute 0 for x and 1000 for y in y=Cbx. y=Cbx1000=Cb01000=C1C=1000 Therefore, the function is y=1000bx Substitute 1 for x and 500 for y in y=1000bx. y=1000bx500=1000b1500=1000bb=5001000b=12 Therefore, the exponential function is y=100012x. c) It is required to given the decay rate. Comparing y=100012x with the general form of exponential equation y=abx. Thus, the value of b is 12 which satisfies 0<b<1. Thus, the decay factor is 12. In percentage it is 50%. Therefore, the decay rate is 50%.