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 Posted: Wed Jun 08, 2016 4:15 pm

Joined: Tue Oct 02, 2007 10:58 am
Posts: 132
DD (who has her Maths GCSE tomorrow morning) is stuck on a question about exponential growth/ decay and neither of us can work out how to do it clearly from the mark scheme.
Can any of you Maths whizzes help please? Guest 55

"Rhys has a beehive. The number of bees is decreasing. There are 1200 at the start of week 5 and 900 at the start of week 7.
Assuming the population is decreasing exponentially, how many bees were there at the start of week 2?"

Please can you explain it as simply as possible with lots of steps.

Thanks!

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 Posted: Wed Jun 08, 2016 4:24 pm

Joined: Mon Feb 12, 2007 1:21 pm
Posts: 11940
Does it really say 'exponentially'? That implies a type of decay not met at GCSE ...

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 Posted: Wed Jun 08, 2016 4:33 pm

Joined: Tue Oct 02, 2007 10:58 am
Posts: 132
Yes- I've copied the question from a past paper- but it's the double pilot so this is from Applications Paper 2 (DD will take 4 altogether). It's mandatory for everyone at her school.

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 Posted: Wed Jun 08, 2016 4:37 pm

Joined: Tue Oct 02, 2007 10:58 am
Posts: 132
I just checked her sheet summarising what they have to be able to do :

it says " you can use multipliers to explore exponential growth and decay" and "you can use exp growth in real life problems" (bees in this case I suppose)

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 Posted: Wed Jun 08, 2016 4:41 pm

Joined: Mon Feb 12, 2007 1:21 pm
Posts: 11940
Which board and which year's paper?

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 Posted: Wed Jun 08, 2016 4:47 pm

Joined: Tue Oct 02, 2007 10:58 am
Posts: 132
It's from Edexcel Linked pair pilot Applications of Maths GCSE paper 2 (Higher) Summer 2015

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 Posted: Wed Jun 08, 2016 4:56 pm

Joined: Mon Feb 12, 2007 1:21 pm
Posts: 11940
OK - I did not do it like the mark scheme.

At the beginning there are B bees.

Start of week 2 there are B x d bees where d is the decay rate

Start of week 3 B x d^2

Start of week 5 B x d^4 = 1200 bees

Start of week 7 B x d^6 = 900 bees

(^ means to the power)

dividing week 7 by week 5 gives d^6/d^4 = 900/1200

ie d^2 = 900/1200 = 3/4

d = root 3/2

Put into one of equations to get B [this did not give me a whole number so it is a bad question imho]

The put B and d into expression for start of week 2.

Does this help?

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 Posted: Wed Jun 08, 2016 5:08 pm

Joined: Tue Oct 02, 2007 10:58 am
Posts: 132
Brilliant, got it! That makes a lot more sense to DD and me than the mark scheme.
Thanks G55

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 Posted: Wed Jun 08, 2016 5:13 pm

Joined: Mon Feb 12, 2007 1:21 pm
Posts: 11940

They have worked backwards from week 5

1200 x 1/decay to get week 4 etc

However they should have checked they got a whole number of bees!

Reminds me of the Monty Python song 'Eric the hallf a bee'

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 Posted: Wed Jun 08, 2016 5:16 pm

Joined: Tue Oct 02, 2007 10:58 am
Posts: 132

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