formula for increasing cost per unit

let's say an item cost x amount. for each item you buy, beyond the first, cost increases by x / 10. the item provides a unit of concern.

so, the problem is that i need to create a chart with the trends, but need to start with the equations.

to use an example (using obviously made up, easy numbers):

a small airplane initially costs $5, and provides a speed of 3. (assuming the factor of increase per plane is taking into account the cost of the space of storage) the second plane would cost $5.50, and provides an additional 3 of speed.

medium plane initially costs $10, with speed of 6. second would cost $11, providing additional 6 speed.

question/concern:
i need to find out a way to see the trends across the next 100 purchases, based on the costs per unit of speed. meaning, first plane costs ($5/3 speed) ~ $1.67. second, ($5.50/6) ~$0.92, and so on.
this applying to each level (small plane, medium plane, large...). then, the graph must show each, small plane's relative amount as one line, medium as another, etc.
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maybe this would work?

initial cost of unit = x; number of units have = n; unit of speed = s
[=(x/10s) + (x/sn)] {derived from: ((x/10)*n + x)/sn)} lol racking my brain here....

I was following you right up until you used the word "trends." That is usually used to refer to analysis of empirical measurements to find an idealized equation to model the data. But you are starting out with an equation. So you can calculate the cost and cost/speed of the nth airplane trivially.

Look at the attached as a starting point. I used slightly different numbers to make things more interesting. When the proportion of price to speed stays the same for different types of planes (as in your example) the cost/speed will be the same regardless of the size of the plane.

Do you need the cost/speed of just the nth plane, or for the 1st to the nth plane combined?

The equation for total cost of n planes where a is the cost of the first plane is, in reduced form:

cost = (9+n)a/10

The cost per speed of the nth plane where s is speed is therefore

cost/speed = (9+n)a/10s

awesome! there is a lot there that i can learn from. but, i see that i'll have to be more specific to achieve my goal. (i've attached the spreadsheet of concern)

essentially, the set up is this:
i have x number of small planes(in spreadsheet as "Bunker"), y number of medium planes("guard towers"), and z number of large planes("anti-aircraft launcher"). (and your numbers are great!) over the next 100 purchases, what is the graphical representation of each cost per unit? so, the problem isn't that i need to see the initial 100 purchases like i inadvertantly lead you to believe, but that i need to see the next 100 (x + 100, etc).

then, i need to find out how to determine how many of each i need to purchase, in order to obtain the cost per unit that the max has...

p.s. : thank you a lot for your help so far, by the way... definitely appreciated!!

anyone? i can't seem to figure out a way to graphically depict what will happen over the next 100 purchases. any help here would be awesome

yes, i understand. i had to take pieces from my major spreadsheet, because it is higher than the allotted forum upload size. but, the major part that i was looking to get the visual representation for is the actual buildings portion. upon changing any of the numbers, it should show how the different purchases causes the rest of the information to change (including the cost per unit-income or defense)

thank you though for looking at it a second time!

update:

i've figured out a way to do what i need to do. concept here is to use vlookup to find the specific numbers i want to use (initial cost, number currently have, cost of next), given the name of the building. ie: [=((VLOOKUP(B30, defensechart, 3, 0)/10)*(VLOOKUP(B30, defensechart, 4, 0))+VLOOKUP(B30, defensechart, 3, 0))/VLOOKUP(B30, defensechart, 2, 0)] so: {lookup building name in the chart, to find initial cost. divide by 10 (rise in cost). multiply that by the number currently have. add to initial cost. divide total by unit of interest (defense, income, etc)}
have another column adding 1 to previous number of buildings (hide columns, since not interested in this, except for the purpose of calculating next building's cost/unit)

then, select the blocks want in graph, and create chart.

attached spreadsheet for additional clerification.

but, thank you very much for responding to this, 6String! the effort was valiant, and i know that my wording probably didn't help in understanding what i was looking for lol