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 solve this problem, we need to calculate the blood alcohol level after 2 hours given that one-fourth of the alcohol in the blood is removed every hour. Let's start by understanding the exponential decay formula.

The formula for exponential decay is given by:
A = A₀ * e^(-kt)

where:
A is the final amount after time t,
A₀ is the initial amount,
e is the base of the natural logarithm (approximately 2.71828),
k is the decay constant,
t is the time in hours.

In this case, the initial amount (A₀) is 200 mg/dL, and the decay constant (k) is ln(1/4). Now we can plug these values into the formula and solve for the final amount (A) after 2 hours.

A = A₀ * e^(-kt)
A = 200 * e^(-ln(1/4) * 2)

Now, let's calculate the final blood alcohol level after 2 hours using this formula.

A = 200 * e^(-ln(1/4) * 2)
A ≈ 200 * e^(-0.6931 * 2)
A ≈ 200 * e^(-1.38629)
A ≈ 200 * 0.2512
A ≈ 50.24 mg/dL

Therefore, after 2 hours, the person's blood alcohol level will be approximately 50.24 mg/dL.