Growth of four items to a approx equal

Ashamaan

New member
Joined
Oct 12, 2018
Messages
2
Hello MathHelp,

This is a problem for one of those RTS/4X games.

We have four values..

1400
690
4030
5920

each of these values is increasing (or decreasing) by

+200
+486
+166
-161 (decreasing)

respectively, per hour.

Is there a formula or factor method I can use to calculate WHEN these values will be equal or almost equal? Like a point where all of them will 4800. In how many hours/minutes?
If the 4th value of decreasing rate complicates matters. We can leave that out and only calculate for the increasing values. I think if we do that it becomes a form LCM problem?
Also when I say the value increases by +200 per hour it means it increases by approx 3.34 per minute, and similarly for the other values too. Trickle growth.

Previously used a graphing method and just found the point where all three intersect.
 
Hello MathHelp,

This is a problem for one of those RTS/4X games.

We have four values..

1400
690
4030
5920

each of these values is increasing (or decreasing) by

+200
+486
+166
-161 (decreasing)

respectively, per hour.

Is there a formula or factor method I can use to calculate WHEN these values will be equal or almost equal? Like a point where all of them will 4800. In how many hours/minutes?
If the 4th value of decreasing rate complicates matters. We can leave that out and only calculate for the increasing values. I think if we do that it becomes a form LCM problem?
Also when I say the value increases by +200 per hour it means it increases by approx 3.34 per minute, and similarly for the other values too. Trickle growth.

Previously used a graphing method and just found the point where all three intersect.
Four lines may not meet at one point.
 
Hello MathHelp,

This is a problem for one of those RTS/4X games.

We have four values..

1400
690
4030
5920

each of these values is increasing (or decreasing) by

+200
+486
+166
-161 (decreasing)

respectively, per hour.

Is there a formula or factor method I can use to calculate WHEN these values will be equal or almost equal? Like a point where all of them will 4800. In how many hours/minutes?
If the 4th value of decreasing rate complicates matters. We can leave that out and only calculate for the increasing values. I think if we do that it becomes a form LCM problem?
Also when I say the value increases by +200 per hour it means it increases by approx 3.34 per minute, and similarly for the other values too. Trickle growth.

Previously used a graphing method and just found the point where all three intersect.

Four lines can meet at one point, but that is a very special case. These four don't; in fact, the first and third don't meet until long after other pairs do, so they are never all close together.

FMH112894.jpg

Algebraically, all you can do is to choose any two of the equations and solve for when they are equal, then see if the others are equal at that time. You will find that they aren't.

Why do you expect the four values ever to be equal? And how did you find a place where "all three intersect"?
 
Four lines can meet at one point, but that is a very special case. These four don't; in fact, the first and third don't meet until long after other pairs do, so they are never all close together.

View attachment 10319

Algebraically, all you can do is to choose any two of the equations and solve for when they are equal, then see if the others are equal at that time. You will find that they aren't.

Why do you expect the four values ever to be equal? And how did you find a place where "all three intersect"?

Is that because the initial values are so far apart?
I thought that. In the past when I used graphs.. the values were not soo far apart from another.

Even so.. for future reference .. When the values are in more feasible. How does one solve such problems non-gprahically.,

Say if all values started with 1200 but the growth rate was as given about? Disregarding the last one that is dicreasing.
 
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