# I can't wrap my head around this word problem!

#### Azaraxzealot

##### New member
I designed this word problem myself in designing a game, but i can't seem to make an equation out of it:

You establish colonies that always grow in population, 1 person per 1 seconds. The more colonies you control, the faster the overall population will increase.
For every colony you control the speed goes up by 0.01 seconds, so if you have 2 colonies you get one person every 0.98 seconds.

Your population stops growing over time as the colonies get "full" then you will need to make new colonies.

depending on the size of the colony the initial population bonus will vary
Tiny: 50 people (100 max)
Med-Small: 75 people (175 max)
Small: 100 people (250 max)
Medium: 150 people (375 max)
Large: 250 people (600 max)

examples: If you have 4 tiny colonies.

-You can have a maximum population of 400.

-Your population grows by 1 person every 0.3 seconds.

-You had a starting population of 200.

Basically, i keep trying to think of an equation that just represents the population size as the dependent variable and the number of colonies increasing the speed of population growth over time as the independent variable

#### crudus

##### New member
colpop=+1-(colnum*.01)

if(colpop>max)
colpop=max

Is this what you mean?

#### Gxas

##### New member
"It never occurred to me to think of space as the thing that was moving"
-Scotty, Star Trek (2009)-

Perhaps think of the problem in a different way?

#### aseelt

##### New member
For that particular example := Population = (50x + (t*(1-0.01x))

Where x is number of tiny colonies, t is time passed

So for 4 tiny colonies := 50 x 4 + t*0.96

Wouldn't your population grow by 0.25 per second because of the four colonies?

For every colony type:= Population = (50x + (t*(1-0.01x)) + (75y + (t*(1-0.01y)) + (100z + (t*(1-0.01z)) + (150a + (t*(1-0.01a)) + (250b + (t*(1-0.01b))

Where x is number of tiny colonies, y is number of medium/small, z is small, a is medium, b is large

Can't quite figure out the maximum constraints

Also shouldn't the larger colonies have a bigger growth rate?

#### Azaraxzealot

##### New member
aseelt said:
For that particular example := Population = (50x + (t*(1-0.01x))

Where x is number of tiny colonies, t is time passed, p

So for 4 tiny colonies := 50 x 4 + t*0.96

Wouldn't your population grow by 0.25 per second because of the four colonies?

For every colony type:= Population = (50x + (t*(1-0.01x)) + (75y + (t*(1-0.01y)) + (100z + (t*(1-0.01z)) + (150a + (t*(1-0.01a)) + (250b + (t*(1-0.01b))

Where x is number of tiny colonies, y is number of medium/small, z is small, a is medium, b is large

Can't quite figure out the maximum constraints

Also shouldn't the larger colonies have a bigger growth rate?
in reality, yes, but i wanted to keep it as simple as possible. like simplified "Stronghold" but with just population management.

but yes, what you provided is VERY helpful.

#### Azaraxzealot

##### New member
crudus said:
colpop=+1-(colnum*.01)

if(colpop>max)
colpop=max

Is this what you mean?
just about. lemme check the equation...
if, after 10 seconds, you have 10.1 colonists when you have just one colony and you started with a tiny colony then your population should be 60.1 (but it wouldn't show the decimal.

and if you had 50 colonies (let's say... 10 tiny, 10 small, and 30 large) then after 10 seconds your population should be (assuming all colonies started at the same time) 4000 initially and after 10 seconds it should be 4050 (because the time is reduced to 1 person every 0.5 seconds instead of the original 1 per second)

i have been thinking about it wrong though. instead of taking away time, i need to be adding MORE people per second.

so the equation would be closer to
t*(1+0.01x)=p

where "x" is the number of colonies, so instead of it subtracting time, it's just adding more people!

#### Azaraxzealot

##### New member
Gxas said:
"It never occurred to me to think of space as the thing that was moving"
-Scotty, Star Trek (2009)-

Perhaps think of the problem in a different way?
you actually brought about a real revelation.

#### aseelt

##### New member
Actually that isn't helpful. Over time you'd get less if you had more colonies.

Example: 3 colonies = t*0.97
For 7 colonies = t*0.93

It should be 1+0.01 times whatever colony number.

EDIT: Ninja'd!

#### Gxas

##### New member
Azaraxzealot said:
Gxas said:
"It never occurred to me to think of space as the thing that was moving"
-Scotty, Star Trek (2009)-

Perhaps think of the problem in a different way?
you actually brought about a real revelation.
I wanted to help, and did so in the only way I knew how; quote movies. I'm glad it worked!

#### Azaraxzealot

##### New member
aseelt said:
Actually that isn't helpful. Over time you'd get less if you had more colonies.

Example: 3 colonies = t*0.97
For 7 colonies = t*0.93

It should be 1+0.01 times whatever colony number.

EDIT: Ninja'd!
ninja'd by me? ;D
in any case, thanks to Gxas and everyone else i was able to figure it out. the thread has run its course

thanks everyone