When doctors prescribe medicine, they must consider how the drug’s effectiveness declines as time passes. If each hour a drug is only 90% as effective as the previous hour, at some point the patient will have to be given another dose in order for the drug to remain effective. If the initial dose was 500 mg and the drug was administered 6 hours ago, how long will it take for the initial dose to reach a level of 150 mg?

The total time for the initial dose of 500 mg to reach a level of 150 mg is approximately 11 hours and 27 minutes

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

The total time for the initial dose of 500 mg to reach a level of 150 mg is approximately 11 hours and 27 minutes

answer: the answer is one of

step-by-step explanation:   we are given to write a proper fraction where the whole is divided into an even number of equal parts less than ten, and an odd number of those parts exist.

an even number less than 10 may be one of 2, 4, 6 or 8. so, the whole may be one of these four evens.

now, an odd number of these parts must exist, so the numerator must be an odd number, one of 1, 3, 5 or 7. it cannot be 9 because then the fraction will become improper.

thus, our fraction may be one of the following