Question

A cup of coffee has approximately 310 mg of caffeine. Each hour, the caffeine in your system decreases by about 35%. How much caffeine would be left in your system after 5 hours? Round to the nearest whole.

Answer 1

∴35.97 mg caffeine would be left in the system after 5 hours.

Explanation:

Given that,

A cup of coffee has approximately 310 mg of caffeine.

Caffeine decrease at a rate 35% per hour.

Exponential Function:

`y(t)=y_0(1-r)^t`

y(t)= Amount caffeine after t hours

`y_0`= Initial amount of caffeine

r= rate of decrease

t = Time in hour.

Here y(t)=?,
`y_0` = 310 mg, r=35%=0.35, t= 5 hours

`y(t)=310(1-0.35)^5`

=35.97 mg

∴35.97 mg caffeine would be left in the system after 5 hours.