Answer:
<u>The total time for the initial dose of 500 mg to reach a level of 150 mg is approximately 11 hours and 27 minutes </u>
Step-by-step explanation:
Initial dose = 500 mg
Let's calculate the effectiveness of the drug hour by hour, this way:
After 1 hour: 90% of 500 = 450 mg
After 2 hours: 90% of 450 = 405 mg
After 3 hours: 90% of 405 = 364.5 mg
After 4 hours: 90% of 364.5 = 328.05 mg
After 5 hours: 90% of 328.05 = 295.25 mg
After 6 hours: 90% of 295.25 = 265.73 mg
After 7 hours: 90% of 265.73 = 239.16 mg
After 8 hours: 90% of 239.16 = 215.24 mg
After 9 hours: 90% of 215.24 = 193.72 mg
After 10 hours: 90% of 193.72 = 174.35 mg
After 11 hours: 90% of 174.35 = 156.92 mg
After 12 hours: 90% of 156.92 = 141.23 mg
Difference between 11 and 12 hours: 156.92 - 141.23 = 15.7 mg
Difference per minute between 11 and 12 hours: 15.7/60 = 0.262 mg
Time to reach a level of 150 mg in minutes after 11 hours = (156.92-150)/0.262
Time to reach a level of 150 mg in minutes after 11 hours = 26.4
<u>The total time for the initial dose of 500 mg to reach a level of 150 mg is approximately 11 hours and 27 minutes </u>
