Question

The concentration (in milligrams per liter) of an antibiotic in the blood is given by the geometric series:

A + Aekt + Ae2kt + + Ae(n − 1)kt

where A is the number of milligrams in one dose of the antibiotic, n is the number of doses, t is the time between doses, and k is a constant that depends on how quickly the body metabolizes the antibiotic. Suppose one dose of an antibiotic increases the blood level of the antibiotic by 0.5 milligram per liter. If the antibiotic is given every 4 hours and
k = −0.853
, find the concentration, to the nearest hundredth, of the antibiotic just before the fifth dose. (Round your answer to two decimal places.)

Answer 1

Since we have a geometric series,

Sn = A * (e^knt - 1)/(e^kt - 1)

So, plug in the numbers and we have

S5 = 0.5 (e^(-0.853*4*5)-1)/(e^(-0.853*4)-1)
= 0.517

Answer 2

Are you a mapuan?

Answer 3

yes

Answer 4

I love you see you next term

Answer 5

thanks:) mapuan here:)