+4 in order for an antibiotic to be effective 5 or more mg/dl must be present in the bloodstream. When do you have to take the antibiotic after the initial dose? Solve algebraically and graphically
Equation: c(t)= 55t/t*2+25
+128408 55t
_______ = 5
t^2 + 25
Multiply both sides by t^2 + 25
55t = 5(t^2 + 25) divide both sides by 5
11t = t^2 + 25 rearrange as
t^2 - 11t + 25 = 0
Using the quaratic fromula
11 ±√[11^2 - 4(1)(25)]
____________________
2
11 ±√[121 - 100]
_______________
2
11 ±√21
________
2
Take the least value of t =
11 - √21
________ ≈ 3.2 hrs
2
Heres the graph : https://www.desmos.com/calculator/ejgdwf1ijg
