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A patient receives 999 mg of a medicine. Each hour, \frac{1}{3}of the medicine in the patient's body decays.

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Anonymous
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  1. Complete the table with the amount of medicine m in the patient's body.
  2. Write an equation representing the number of mg of the medicine m, in the patient's body h hours after receiving the medicine.
  3. Use your equation to find m when h = 15 . What does this mean in terms of the medicine?

      

Sangeetha Pulapaka
0
  1. The function representing the number of mg of the medicine m, in the patient's body h hours after receiving the medicine.where t is the number of hours after receiving the medicine is  m = 999. (\frac{2}{3})^{h} This is because if \frac{1}{3} decays then we are left with \frac{2}{3}. Plugging in  t = 0 then the medicine left in the body will be 999. If h = 1, then we have m = 666

          If h = 2, plug in h= 2 in the equation  and we get 999. (\frac{2}{3})^{2} = 444 to get the medicine left as 444. Plugging in h = 3 in the    

          equation and get 999. (\frac{2}{3})^{3}= 296 .This is how you complete the table.  

        

      2.The equation representing the number of mg of the medicine m, in the patient's body h hours after receiving the medicine is 

      m = 999.(\frac{2}{3})^{h}

      3.Plugging in h = 15  in the equation 999.(\frac{2}{3})^{15} = \frac{32,735,232}{14,348,907} \approx 2.29 This means that the quantity of the medicine is almost zero.


Skills you may want to recall:

What is an exponential function

https://www.purplemath.com/modules/expofcns.htm

How to complete an exponential function table

https://learnzillion.com/lesson_plans/7695-write-and-graph-an-exponential-function-by-examining-a-table/