divide that by 128 to get 12.5
if would take 12.5 weeks for the inventory to reduce from 3600 to 2000.
multiply 128 by 12.5 and you get 1600.
that's the reduction required to get from 3600 to 2000.
you can use the arithmetic progression formula to get the same answer.
that formula is An = A1 + (n-1) * d
An = 2000
A1 = 3600
d = -128 because you are subtracting 128 each time rather than adding.
formula becomes:
2000 = 3600 + (n-1) * -128
subtract 3600 from both sides of the equation to get:
2000 - 3600 = (n-1) * -128
simplify to get:
-1600 = (n-1) * -128
divide both sides by -128 to get
-1600 / -128 = (n-1)
solve for (n-1) to get 12.5
the formula becomes:
2000 = 3600 * 12.5 * -128
evaluate to get:
2000 = 2000
this confirms the solution is correct
either way you get the same answer, although use of the arithmetic progression formula might be a little trickier.
the basic solution i used was find the difference and divide it by 128 to get the number of weeks.
3600 - 2000 = 1600
1600 / 128 = 12.5
if you graph the equation of y = 3600 - 128 * x, it would look like this:
x represents the number of weeks.
y represents the the inventory after the number of weeks.
when x = 0, you have 3600.
when x = 12.5, you have 2000.