Ok as always happens im a bit stumped by a question in my HNC.

The question is as follows:-

A firm starts work with 110 employees for the 1st week. The number
of the employees rises by 6% per week. How many persons will be
employed in the 20th week if the present rate of expansion continues.

So far the questions have been reasonably straightforward but this one throws in a percentage rise all through the progression which i am unsure of how to deal with.

Cheers all 🙂

Isn’t it basically a compound interest type question? You could use the same formula.

http://math2.org/math/general/interest.htm

Would it not just be 110*1.06^20?

I’ve only got an O Level, and that was decades ago so don’t take my word for it!

The number of employees is

110 x 1.06^n

Where n is the number of weeks.

So 353. Assuming that you want to keep things in whole numbers.

Compound interest would be one example.

Week 0 = 110
Week n = 110 x (1.06^n)

Cheers, Rich

Clearly far too slow!

johnners – you need to compund it, because the growth rate is applied to an ever growing workforce.

I thought raising 1.06 to the power of 20 was doing the compounding.

edit – the last 2 posts agree with me – now I’m confused.
edit edit – and now jon1973 has removed his post leaving me looking like I’m arguing with myself. What an utter cad!
edit edit edit – now he’s said sorry and I look like a cad.

110 + 6% = 116.6.
116.6 + 6% = 123.59.
123.59 + 6% = 131 etc. Rounding where appropriate.

yes, sorry….retracted 😳

Ok that makes sense, but as i am working on a topic to do with AP and Geometric progression i assumed i would be having to apply these figures to a seperate set of rules ie, r=an+1/an

Not sure if it’s the best of questions really – on the basis that you can’t employ a fraction of a person, is it necessary to deal in whole numbers for each year, rather than just at the end of the calculation, which would give a different answer?
Or am I complicating things?

Trek, i think i have it figured. I’m heading out but will give this a blast tomorrow when i can focus properly. Geometric progression involves ratios a far as I’m aware but i still have a fair bit of work to do to understand it fully 🙂

on the basis that you can’t employ a fraction of a person

Based on the amount of time some spend on here at work, I think quite a few employers do.

You can employ fractions of people. Its called part time working.

But the question is unclear as it says “persons” and not FTEs so maybe answer the question twice to hedge your bets!

Once as n = 110 x (1.06^n)

Once as week 1 = 110 x 1.06 = 116
week 2 = 110 x 1.06 = 122 etc

But is 110 + 6% in whole people 116 people with 0.6 of a persons work remaining or 117 people with 0.4 people over staffed?

Makes quite a difference as with fractions of people there are 352.8 staff, rounding down there are 334 staff, rounding to the nearest whole person there are 354 staff and rounding up there are 369 staff.

I’d answer it all four ways!

you have forgotten the minus one at the end of each calculation. Mr fetch – you! you’re fired for over complicating the problem and wasting my time . 🙂
time is money.

OK gotta bump this one, worked out using the Geometric progression formula to as follows S{20} = 110(1-1.06^20) / 1-1.06

Something is pretty wrong and my heed is bouncing 🙂

Does depend if you need to do it ‘real world’ in which case you need do round up to a whole person after each week, no clue if you can do that with fancy maths though.

Finally got it, i had the formula the wrong way round woooohoooooo 🙂

Damn it the next question is even worse 🙁