Hi,
Please be kind. First time user.
I've got a formula as below. It describes the simple pharmokinetics of dosage and response. On day 1, there are no terms to sum. On day 2, there is one summation term. On day 3, there are two summation terms and so on. More weightage is provided to w(i) closer to day of calculation and lesser to those earlier through the exponential term.
i (lower limit) always starts at 1
The values of days n (upper limit) are stored in rows of column C beginning at C2.
The values of w for each day are stored in rows of column D beginning at D2
The value of the function f
are to be computed in Column E beginning at E2
This is the way I interpret the manual computation by hand. I offer an example:
Let's say for simplicity that constants k1 and tau1 are set to 1
Let's say we set first 4 rows of n as 1,2,3,4.
Let's say we set first 4 rows of w as 10.20,30,40
When n = 1, computation does not exist (?)
When n = 2, f(2) = 10 x e^(-1) = 3.678
When n = 3, f(3) = 10 x e^(-2) + 20 x e^(-1) = 8.711
When n = 4, f(4) = 10 x e^(-3) + 20 x e^(-2) + 30 x e^(-1) = 14.240
I've tried to compute f in Excel with the following formula :
$B$4*SUMPRODUCT(D2*EXP(-(ROW(<wbr style="font-family: Arial, Helvetica, sans-serif;">INDIRECT("1:"&MAX(1,C2-1)))-1)<wbr style="font-family: Arial, Helvetica, sans-serif;">/$B$3))
This gives me
f(1) = 10
f(2) = 27.35758882
f(2) = 45.09644173
f(4) = 62.12007171
The result does not match up with the manually results (or my interpretation of the math).
Could someone please help shed some light on how I could correct this? Been really breaking my head over this. Thank you.
Please be kind. First time user.
I've got a formula as below. It describes the simple pharmokinetics of dosage and response. On day 1, there are no terms to sum. On day 2, there is one summation term. On day 3, there are two summation terms and so on. More weightage is provided to w(i) closer to day of calculation and lesser to those earlier through the exponential term.
i (lower limit) always starts at 1
The values of days n (upper limit) are stored in rows of column C beginning at C2.
The values of w for each day are stored in rows of column D beginning at D2
The value of the function f
are to be computed in Column E beginning at E2This is the way I interpret the manual computation by hand. I offer an example:
Let's say for simplicity that constants k1 and tau1 are set to 1
Let's say we set first 4 rows of n as 1,2,3,4.
Let's say we set first 4 rows of w as 10.20,30,40
When n = 1, computation does not exist (?)
When n = 2, f(2) = 10 x e^(-1) = 3.678
When n = 3, f(3) = 10 x e^(-2) + 20 x e^(-1) = 8.711
When n = 4, f(4) = 10 x e^(-3) + 20 x e^(-2) + 30 x e^(-1) = 14.240
I've tried to compute f
in Excel with the following formula : $B$4*SUMPRODUCT(D2*EXP(-(ROW(<wbr style="font-family: Arial, Helvetica, sans-serif;">INDIRECT("1:"&MAX(1,C2-1)))-1)<wbr style="font-family: Arial, Helvetica, sans-serif;">/$B$3))
This gives me
f(1) = 10
f(2) = 27.35758882
f(2) = 45.09644173
f(4) = 62.12007171
The result does not match up with the manually results (or my interpretation of the math).
Could someone please help shed some light on how I could correct this? Been really breaking my head over this. Thank you.
