series and find closed form help please

[oxnutnet]

series and find closed form help please (edited)

i'm in a collage , studying sequence and series.


Prednisone is often prescribed for acute asthma attacks. For 5 mg tablets, typical instructions are: “Take 8 tablets the first day, 7 the second, and decrease by one tablet each day until all tablets are gone.” Prednisone 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 prednisone in the body
the exponential decay is formed
so i think ...
...........(i) 24 hours after taking the first dose (of 8 tablets), right before taking the second dose (of 7 tablets)
is the answer "8*5e^-kx" ? ....i don't know what k is.
...........(ii) Immediately after taking the second dose (of 7 tablets).
"8*5e^-kx+ 7*5e^-kx" ?
...........(iii) Immediately after taking the third dose (of 6 tablets).
"8*5e^-kx+ 7*5e^-kx+ 6*5e^-kx" ?
...........(iv) Immediately after taking the eighth dose (of 1 tablet).
"8*5e^-kx+ 7*5e^-kx+ 6*5e^-kx + ... + e^-kx" ?
...........(v) 24 hours after taking the eighth dose.
i don't know how to find it.
...........(vi) n days after taking the eighth dose.
i don't know how to find it.

(b) Find a closed form for the sum T = 8x⁷7+ 7x⁶ + 6x⁵ + ••• + 2x + 1, which is the number of prednisone tablets in the body immediately after taking the eighth dose.
T_n = nx^(n-1) ??

(c) If a patient takes all the prednisone tablets as prescribed, how many days after taking the eighth dose is there less than 3% of a prednisone tablet in the patient's body? The half-life of prednisone is about 24 hours.
i don't know how to find it.

(d) A patient is prescribed n tablets of prednisone the first day, n - 1 the second, and one tablet fewer each day until all tablets are gone. Write a formula that represents T_n, the number of prednisone tablets in the body immediately after taking all tablets. Find a closed form sum for T_n.

 

[Deleted member 4993]

i can't write the exponential formula and can't find the answer help please...


Prednisone is often prescribed for acute asthma attacks. For 5 mg tablets, typical instructions are: “Take 8 tablets the first day, 7 the second, and decrease by one tablet each day until all tablets are gone.” Prednisone 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 prednisone in the body
...........(i) 24 hours after taking the first dose (of 8 tablets), right before taking the second dose (of 7 tablets).
...........(ii) Immediately after taking the second dose (of 7 tablets).
...........(iii) Immediately after taking the third dose (of 6 tablets).
...........(iv) Immediately after taking the eighth dose (of 1 tablet).
...........(v) 24 hours after taking the eighth dose.
...........(vi) n days after taking the eighth dose.


(b) Find a closed form for the sum T = 8x⁷7+ 7x⁶ + 6x⁵ + ••• + 2x + 1, which is the number of prednisone tablets in the body immediately after taking the eighth dose.

(c) If a patient takes all the prednisone tablets as prescribed, how many days after taking the eighth dose is there less than 3% of a prednisone tablet in the patient's body? The half-life of prednisone is about 24 hours.

(d) A patient is prescribed n tablets of prednisone the first day, n - 1 the second, and one tablet fewer each day until all tablets are gone. Write a formula that represents T_n, the number of prednisone tablets in the body immediately after taking all tablets. Find a closed form sum for T_n.

Are you saying that you do not know how to even start to solve this problem?

What is the equation for "exponential decay"? - search your text-book or google for answer. Then tell us what it is and what does each variable mean in that equation.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...217#post322217

We can help - we only help after you have shown your work - or ask a specific question (not a statement like "Don't know any of these")

Please share your work with us indicating exactly where you are stuck - so that we may know where to begin to help you.

 

[oxnutnet]

Are you saying that you do not know how to even start to solve this problem?

What is the equation for "exponential decay"? - search your text-book or google for answer. Then tell us what it is and what does each variable mean in that equation.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...217#post322217

We can help - we only help after you have shown your work - or ask a specific question (not a statement like "Don't know any of these")

Please share your work with us indicating exactly where you are stuck - so that we may know where to begin to help you.

Thank you for suggestion. I will edit the post