Q:

Doug drank a soda with 130 mg of caffeine. Each hour, the caffeine in the body diminishes by about 12%.a. Write a formula to model the amount of caffeine remaining in Doug’s system each hour.

Accepted Solution

A:
Answer:Caffeine remains in Doug’s system after n hours, c(n) = 130 x 0.88ⁿ mgStep-by-step explanation:Doug drank a soda with 130 mg of caffeine.Caffeine drank = 130 mg Each hour, the caffeine in the body diminishes by about 12%.Reduction of caffeine per hour = 12 %Let c(n) be the caffeine remains in Doug’s system after n hours.[tex]\texttt{Caffeine remaining in Doug’s system after 1 hour =}130-\frac{12}{100}\times 130=0.88^1\times 130mg\\\\\texttt{Caffeine remaining in Doug’s system after 2 hours =}0.88^2\times 130mg\\\\\texttt{Caffeine remaining in Doug’s system after 3 hours =}0.88^3\times 130mg\\\\\texttt{Caffeine remaining in Doug’s system after n hours =}0.88^n\times 130mg[/tex]Caffeine remains in Doug’s system after n hours, c(n) = 130 x 0.88ⁿ mg