after an antibiotic tablet taken

Question

2) After an antibiotic tablet is taken, the concentration of the antibiotic in the bloodstream is modeled by the function mathcal C(t)=8(e^ -0.44 -e^ -0.64 ) where the time is measured in hours and C is measured in mu*g / (mL) What is the maximum concentration of the antibiotic during the first 12 hoursUse calculus to answer this. 3 polnts)

Answer 1

C(t) = 8(e^-0.44t - e^-0.64t)

C'(t) = 8(-0.44/e^0.44t + 0.64/e^0.64t) = 8(-0.44e^0.64t + 0.64e^0.44t) / e^1.08t)

C'(t) = 0 when 0.44e^0.64t = 0.64e^0.44t

So, e^0.2t = 16/11

0.2t = ln(16/11)

t ≈ 1.87

When 0<t<1.87, C'(t)>0. So, C(t) is increasing.

When t>1.87, C'(t)<0. So, C(t) is decreasing.

Maximum when t = 1.87

Maximum concentration = C(1.87). Plug into your calculator to get the answer.