Maths Question - Need help

Helpneeded86

Probably a simple question for most of ye. I am taking a % change from year end 2011 to year end 2012 and year end 2012 to year end 2013.

The first year gives me a change of 28% and the second year 15.62%.

My overall percentage stands at 14.68 and I need to see where based on previous % increases that 14.68 will stand at by 2019.

What is the best model to produce this?

Fish Finger Pie

Logarithms.

Helpneeded86

From googling I get the basic principle is that how man X does it take to get something in to Y. How do I incorporate the previous percentage movements in to this?

Thanks for the reply.

srsly78

It's not multiplication, it's exponentiation. X to the power of Y, not X multiplied by Y.

Helpneeded86

To be honest I am absolutely clueless on the subject where is the best place to start. There would be nothing so simple as an online calculator I could input the information into?

Yakuza

OP, can you clarify what you mean by overall percentage? Are you trying to project what the percentage change will be by 2019 based on two known percentage changes? Some context and extra info will help anyone trying to point you in the right direction.

Helpneeded86

Yakuza wrote: »

OP, can you clarify what you mean by overall percentage? Are you trying to project what the percentage change will be by 2019 based on two known percentage changes? Some context and extra info will help anyone trying to point you in the right direction.

ya I have realised that Il update the thread soon thanks.

Blackpanther95

The whole question might be best.

Helpneeded86

It is not a set out question it is something I am trying to get a projection for myself.

Il set out as clearly as I can all I know and what I need to know.

Company has 289 people. 37 of these are females.

Females have rose from 25-32 from Jan 2011-Jan 2012 and from 32-37 from Jan 2012 - Jan 2013.

We need female representation to be 40% by Jan 2020.

Based on these two % increases where does Female representation look to be by this date?

What % increase is needed to achieve 40%?

We are assuming that teh company will replace current workers with females and there will be no increase in the amount of workers in the company.

Hope this is a little clearer.

Yakuza

That's hard to model easily. Is the number of employees going to be constant? Are you only going to hire females from now on? (This might put you on dodgy grounds discrimination-wise). Are you going to stick with the number of males you have now and only hire females (and assuming none of the males leave).

Percentage increases are kinda meaningless when all parts of the sum can change (no. of males, no. of females, total employees).

There are many ways to model this, it's hard to give a definitive answer.
Assuming you only hire females from now on, and no males leave: currently, you have 252 males. If females are to make up 40% of the workforce, then your total workforce must be 420 (252/60%), so you will have 252 males and 168 females. To go from 37 females to 168 in approximately 6 years means you'll have to hire a net amount of roughly 22 females a year.

micar

Read Douglas Adams. He says the answer is 42.

Helpneeded86

Yakuza wrote: »

That's hard to model easily. Is the number of employees going to be constant? Are you only going to hire females from now on? (This might put you on dodgy grounds discrimination-wise). Are you going to stick with the number of males you have now and only hire females (and assuming none of the males leave).

Percentage increases are kinda meaningless when all parts of the sum can change (no. of males, no. of females, total employees).

There are many ways to model this, it's hard to give a definitive answer.
Assuming you only hire females from now on, and no males leave: currently, you have 252 males. If females are to make up 40% of the workforce, then your total workforce must be 420 (252/60%), so you will have 252 males and 168 females. To go from 37 females to 168 in approximately 6 years means you'll have to hire a net amount of roughly 22 females a year.

Ya I understand the complexity of this but I can outline this in the limitations of my study. The plan is not to increase the workforce as part of this calculation as the company should realistically have the correct amount of workers in place currently. If an increase in the workers happens then it is solely to achieve the objective.

I need to go from 37 to 116 not 168?

The cumulative increase for this to happen is 213.5%. I need to break this down as a year on year increase. How do I do this ?

I understand there is a lot of complexities around this but I can outline these issues.

Blackpanther95

okay so I tried an exponetial model:
let x(t) be the number of females at time t: t=0 is 2011 then x(0)=25 and x(1)=32 and x(2)=37
so the solution is of the form x(t)=Ae^(kt)
it is simple to show A=25, and k=0.15 approx.
hence x(t)=25e^(0.15t) which seems reasonable enough, as the number of females increases the %increase slows down.
so x(t)=40%*289=115.6 =>t=10.21 so in year 11 you'll have 40% females i.e. 2022
x(9)=25e^(0.15*9)=96.44 or 33% females in year 9.
I would recommend typing the equation into wolframalpha and obserivng the solution to see does it look alright.
The problems are x(t)->inf as t->inf. you might want to use a more sophisticated DE to find a more sophiscated solution i.e. x(t)->a*289 as t->inf 0<a<100. This model is used in population statistics.