Final answer:
In 13 hours, the drug concentration decreases by a factor of about 3.472, which is not one of the multiple-choice options provided. The calculation reveals a potential error in the options; however, the closest correct option is D) 0.37.
Step-by-step explanation:
The student has asked what factor the concentration of a drug decreases in 13 hours if it has a half-life of 9 hours. We can solve this problem using the half-life formula for exponential decay which is:
C(t) = C0 * (1/2)^(t/t1/2)
Where:
- C(t) is the final concentration after time t
- C0 is the initial concentration
- t is the time elapsed
- t1/2 is the half-life of the substance.
In this case, we don't need the initial concentration because we are looking for the ratio (factor) by which the concentration decreases. We can set C0 to 1 for simplicity:
C(13) = 1 * (1/2)^(13/9) = (1/2)^(1.4444) ≈ 0.288
After 13 hours, the concentration decreases by approximately 0.288, therefore, the factor by which the concentration decreases is around 1/0.288 ≈ 3.472. This is not one of the answer choices provided, which indicates an error either in the question alternatives or in the calculation. However, the closest correct option from the given choices by rounding is:
D) 0.37