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.

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

Step-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.

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

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)