At 10a.m. you consume an energy drink containing 800mg of caffeine. if the half-life of caffeine is 5.7 hours, how much caffeine is in your body at 7p.m.?

268 mg

Step-by-step explanation:

Let A₀ = the original amount of caffeine

The amount remaining after one half-life is ½A₀.

After two half-lives, the amount remaining is ½ ×½A₀ = (½)²A₀.

After three half-lives, the amount remaining is ½ ×(½)²A₀ = (½)³A₀.

We can write a general formula for the amount remaining:

A =A₀(½)ⁿ

where n is the number of half-lives .

n = t/t_½

Data:

  A₀ = 800 mg

    t₁ = 10 a.m.

   t₂ = 7 p.m.  

t_½ = 5.7 h

Calculations:

(a) Calculate t

t = t₂ - t₁ = 7 p.m. - 10 a.m. = 19:00 - 10:00 = 9:00 = 9.00 h

(b) Calculate n

n = 9.00/5.7 = 1.58

(b) Calculate A

A = 800 × (½)^1.58 = 800 × 0.334 = 268 mg

You will still have 268 mg of caffeine in your body at 10 p.m.