Mcr Pod 1 (ans)

POD 1. You have an ear infection and are prescribed to take 250 mg of ampicillin four times a day. It is known that at the end of 6 h, about 4% of the drug is still in the body. What quantity of the drug is in the body after a. The third dose? b. The twelfth dose? c. The nth dose? Write your answer to three decimal places please t1  250

t2  0.04  t1   250  0.04  250   250

t3  0.04(t2 )  250  0.04  0.04  250   250   250  0.042  250   0.04  250   250

t4  0.04  t3   250  0.04  0.042  250   0.04  250   250   0.043  250   0.042  250   0.04  250   250 . . . tn  0.04  tn 1   250  0.04  0.04n  2  250   0.04n 3  250   ...  0.04  250   250   250  1  0.041  0.042  ...0.04n1 



tn  250 1  0.041  0.042  ...0.04n 1



 0.04n  1    0.04  1 

 250 

Since -1 < r < 1 we use form  1  0.04n    1  0.04 

 250 

Third Dose  0.043  1    0.04  1 

t3  250 

 260.4

20th Dose  0.0412  1    0.04  1 

t20  250 

 260.417  1  0.0412    1  0.04 

t20  250 

 260.417

2. If  1  3  5  ...  p    1  3  5  ...  q    1  3  5  ...  19  where p and q are odd positive integers, evaluate p + q Lets assume that p < q 10  1  19  2  100

1  3  5  ..  19 

n 2

 1  3  5  ...  p    1  3  5  ...  q   1  1  p  

n2  1 q 2

p 1 2 q 1 n2  2 n1 

2

2

n1 n p 1   q 1   1  p   2  1  q       2 2  2   2 

We know that the only two integer values that when squared equal 100 are 8 and 6. Therefore, assuming that p < q p 1 6 2 p  11

11 + 15 = 26

q 1 8 2 q  15