- #1

mundane

- 56

- 0

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.