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 in the blood decays exponentially over time.

We are given that after several drinks, the person has a blood alcohol level of 200 mg/dL. Let's denote this initial blood alcohol level as B₀ = 200 mg/dL.

The problem states that one fourth of the alcohol is removed every hour, which means that after each hour, the blood alcohol level decreases by 25% (or one fourth) of the remaining alcohol.

Using exponential decay, we can represent the blood alcohol level after time t (in hours) as:

B(t) = B₀ * (1 - r)^t

Where:
- B(t) represents the blood alcohol level after time t,
- B₀ is the initial blood alcohol level,
- r is the decay rate (in this case, r = 0.25),
- t is the time in hours.

Now, we can plug in the values and calculate the blood alcohol level after 2 hours.

B(2) = B₀ * (1 - r)^2

Substituting B₀ = 200 mg/dL and r = 0.25:

B(2) = 200 * (1 - 0.25)^2

Simplifying the expression:

B(2) = 200 * (0.75)^2
B(2) = 200 * 0.5625
B(2) = 112.5 mg/dL

Therefore, the person's blood alcohol level after 2 hours would be approximately 112.5 mg/dL.