Final answer:
To determine how long it will take for there to be 17mg of aspirin in the bloodstream, we need to solve an exponential decay equation using logarithms. The needed equation is set up using the initial amount of aspirin (75mg), the remaining amount after 4 hours (74%), and the final desired amount (17mg). By solving this equation, we find the time required to reach 17mg of aspirin in the bloodstream.
Step-by-step explanation:
The student is asking about the time it takes for a specific amount of aspirin to remain in the bloodstream based on its elimination rate. Given that 74% of the aspirin remains after 4 hours, we need to use a logarithmic decay function to determine when only 17mg will be left. This requires understanding exponential decay and half-life calculations in chemistry, which often involve logarithms.
First, let's find out the half-life of aspirin using the given information. If 74% remains after 4 hours, then 26% has been eliminated. Since we're looking for when the amount is reduced to 17mg from an initial dose of 75mg, the calculations involve setting up and solving an exponential decay equation where the amount A at time t is given by the formula A = A0 * (0.74)^(t/T), where A0 is the initial amount, A is the remaining amount at time t, and T is the time for 74% to remain (4 hours in this case).
To find the time when there's 17mg left, we set A = 17mg, A0 = 75mg, and solve for t:
17 = 75 * (0.74)^(t/4).
This equation can be solved by taking logarithms on both sides and isolating t. The final step is to use a calculator to compute the value of t, which will give us the time it takes for there to be 17mg of aspirin in the bloodstream.