After several drinks, a person has a blood alcohol level of 200 mg/dL (milligrams per deciliter). If the amount of alcohol in the blood decays exponentially, with one fourth being removed every hour, find the person's blood alcohol level after 2 hours.

To find the person's blood alcohol level after 2 hours, we need to understand how the amount of alcohol decays exponentially over time.

Let's break down the problem and use the given information:

Initial blood alcohol level: 200 mg/dL
Decay rate: one fourth (1/4) being removed every hour
Time: 2 hours

To calculate the blood alcohol level after 2 hours, we'll use the formula for exponential decay:

C(t) = C₀ * (1/4)^(t/h)

Where:
C(t) is the blood alcohol level at time t
C₀ is the initial blood alcohol level
t is the elapsed time
h is the half-life or decay rate

In this case, since one-fourth (1/4) is being removed every hour, the half-life (h) is 1 hour.

Now let's plug in the values and calculate:

C(t) = 200 * (1/4)^(2/1)

First, simplify the exponent:

C(t) = 200 * (1/4)^2

Next, evaluate the exponent:

C(t) = 200 * (1/16)

Finally, calculate the result:

C(t) = 12.5 mg/dL

Therefore, after 2 hours, the person's blood alcohol level will be 12.5 mg/dL.