Question

A cup of soda you drank has 150 milligrams of caffeine. If each hour, the amount of caffeine in your body decreases by about 15%, how much caffeine will be in your body in 3 hours ? Round to the hundredths place. Omit units.

Answer 1

After 3 hours, 92.12 milligrams of caffeine will remain in the body from an initial amount of 150 milligrams, considering a 15% hourly decrease in caffeine level.

Step-by-step explanation:

To calculate the amount of caffeine remaining in your body after 3 hours, when the starting amount is 150 milligrams and it decreases by 15% each hour, you can use the formula for exponential decay:

`C(t) = C0 × (1 - r)^t`

Where:

• C(t) is the amount of caffeine remaining after t hours
• C0 is the initial amount of caffeine
• r is the rate of decrease (15% or 0.15)
• t is the time in hours

Plugging in the values, we get:

`C(3) = 150 × (1 - 0.15)^3`

`C(3) = 150 × (0.85)^3`

C(3) = 150 × 0.614125

C(3) = 92.119 (rounded to hundredths place)

Therefore, 92.12 milligrams of caffeine will remain in the body after 3 hours.