Acetaminophen is a medicine commonly used to relieve pain and reduce fever. For a patient who takes an initial dose of 0.325 grams, the function A(t)=0.325(0.76)t models the amount of acetaminophen, in grams, in the body after t hours. According to the model, how does the amount of acetaminophen in the body change over time?
According to the model A(t)=0.325(0.76)t, the amount of acetaminophen in the body changes over time by multiplying the initial dose of 0.325 grams by the exponential factor (0.76)t.
As t increases, the exponential factor (0.76)t increases as well. This means that the amount of acetaminophen in the body also increases.
However, it is important to note that (0.76)t is less than 1 for all positive values of t. This means that the exponential factor is continuously getting smaller as t increases, but it will never reach 0. This implies that the amount of acetaminophen in the body will continue to increase, but at a decreasing rate.
In summary, the amount of acetaminophen in the body initially increases rapidly and then continues to increase, but at a decreasing rate over time.