- #1
mundane
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Hi, I am a sophomore in college and, well I have to do this problem that makes no sense to me... I really don't know where to start. Would you help, and maybe explain how to develop these equations as well?
It says...
"For 5 mg some medication, the instructions on the bottle are: Take 8 tablets on Day 1, 7 on Day 2, and decrease by one tablet each day until all tablets are gone. This medication decays exponentially in the body, and 24 hours after taking k mg, there are kx mg in the body.
a) Write formulas involving x for the amount of medication in the body.
- 24 hours after taking the first dose (8 tablets), right before taking the second dose (7 tablets).
- Immediately after taking the second dose. (7 tablets).
- Immediately after taking the eighth dose (1 tablet)
- n days after taking the eighth dose.
b) Find a closed form for the sum T = 8x^7 + 7x^6 + 6x^5 + ... + 2x + 1, which is the number of medication tablets in the body right after taking the eighth dose.
c) If a patient takes all the medication as prescribed, how many days after taking the eighth dose is there less than 3% of a medication tablet in the patient's body? The half-life of the medication is about 24 hours.
d) A patient is prescribed n tablets of medication the first day, n-1 the second, and one tablet fewer each day until all tablets are gone. Write a formula that represent T(sub)n, the number of medication tablets in the body right after taking all tablets. Find a closed form for T(sub)n."
I have tried for hours and am so frustrated.
It says...
"For 5 mg some medication, the instructions on the bottle are: Take 8 tablets on Day 1, 7 on Day 2, and decrease by one tablet each day until all tablets are gone. This medication decays exponentially in the body, and 24 hours after taking k mg, there are kx mg in the body.
a) Write formulas involving x for the amount of medication in the body.
- 24 hours after taking the first dose (8 tablets), right before taking the second dose (7 tablets).
- Immediately after taking the second dose. (7 tablets).
- Immediately after taking the eighth dose (1 tablet)
- n days after taking the eighth dose.
b) Find a closed form for the sum T = 8x^7 + 7x^6 + 6x^5 + ... + 2x + 1, which is the number of medication tablets in the body right after taking the eighth dose.
c) If a patient takes all the medication as prescribed, how many days after taking the eighth dose is there less than 3% of a medication tablet in the patient's body? The half-life of the medication is about 24 hours.
d) A patient is prescribed n tablets of medication the first day, n-1 the second, and one tablet fewer each day until all tablets are gone. Write a formula that represent T(sub)n, the number of medication tablets in the body right after taking all tablets. Find a closed form for T(sub)n."
I have tried for hours and am so frustrated.