Question

You drink a beverage with 120 mg of caffeine. Each hour, the caffeine in your system decreases by about 12%. How long until you have 10mg of caffeine?

Answer 1

Answer:

  19.44 hours, about 19 hours 26 minutes

Step-by-step explanation:

The exponential equation that describes your caffeine level can be written as ...

  c(t) = 120·(1 -0.12)^t . . . . where t is in hours and c(t) is in mg

We want to find t for c(t) = 10, so ...

  10 = 120(0.88^t)

  10/120 = 0.88^t . . . . . . . divide by 120

  log(1/12) = t·log(0.88) . . . take logarithms

  t = log(1/12)/log(0.88) ≈ 19.4386

It will take about 19.44 hours, or 19 hours 26 minutes, for the caffeine level in your system to decrease to 10 mg.