Question

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.

Answer 1

Caffeine remains in Doug’s system after n hours, c(n) = 130 x 0.88ⁿ mg

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.

`\texttt{Caffeine remaining in Doug’s system after 1 hour =}130-(12)/(100)* 130=0.88^1* 130mg\\\\\texttt{Caffeine remaining in Doug’s system after 2 hours =}0.88^2* 130mg\\\\\texttt{Caffeine remaining in Doug’s system after 3 hours =}0.88^3* 130mg\\\\\texttt{Caffeine remaining in Doug’s system after n hours =}0.88^n* 130mg`

Caffeine remains in Doug’s system after n hours, c(n) = 130 x 0.88ⁿ mg