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Forgive me ignorance in advance for this question as I'm not a mathematician in any respect. I can't even pretend to give correct terminology so I'll just give an example:

We're a a retail company. We buy 1000 units of products. We sell an equal amount of these products each day and by day 90 we have 0 products. How do I calculate how many units we have on average each day over that 90 days? (even better would be calculating the average units on hand in month 1, month 2, and month 3.

I can calculate this manually but I'm sure there must be a nice formula for this (I'll be putting the formula ultimately into Excel if that makes a difference)

Thank you so much in advance!

David-Dj Bryant
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1 Answers1

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Since the rate of change is constant, in $90$ days you sell $1000$ units, in $1$ day you sell $\frac{1000}{90} = \frac{100}{9}$ or $11.111 \cdots$ units.

As an extension, you can make a formula to find how many units you have in a given day, or how many days it would take to reach a given unit.

Let $y$ be the number of units, and $x$ be the number of days. The equation of a line is $y = mx+b$. Then the constant rate of change – the slope $m$ is $\frac{100}{9}$ as in the first part.

We now have $y = \frac{100}{9}x + b$. Since we know that in $90$ days, there will be $0$ units, we can substitute $x = 90$, $y = 0$ into the equation to get $0 = \frac{100}{9} \cdot 90 + b$. This is $0 = 1000+b$, so $b = 1000$. Putting it all together, we have $y = \frac{100}{9}x + 1000$. Now you can substitute $x = 30, 60, 90$ to find how how many units you have at the end of each month.

Toby Mak
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