Stumped

[Taz1981]

Hi,

Can somebody please help with this question which appeared on a test 11+ cem paper and what to search in google to find similar ones. Thank you

The number of ants in a colony triples every 4 minutes. If there are 4 ants in the colony at 15:32, how many ants are there in the colony at 16:00?

[solimum]

That's exponential growth for you....

Best way to understand is to make a table:

Time Ants
15:32 4
15:36 4x3 = 12
15:40 4x3x3 = 36
15:44 etc

In the LH column the time goes up by 4 min intervals, you can see how the multiples of three build up on the RHS - can you spot the pattern?

[Taz1981]

Thanks, this was in a 8 min test, how on Earth can a 10 year old answer this within 90 seconds?

[Taz1981]

Thanks for this but this table will take a long time and the tests are only 10 min tests. How can a child work this out within 60-90 seconds? Is there a quicker formula or should they just skip questions like these for the 11+ exams.

[olucares]

Bear in mind that some questions will be easier to answer and may only take 20-25 secs, which may then afford the child a bit more time on questions like this.

[Surferfish]

Solimum's suggestion is a good way to explain and understand what's going on.

But if you want to save time, once you get the idea there's no real need to make a table showing the number after every 4 minute interval.

You should be able to see that at 16:00, without writing out all the intermediate steps, the total number is 4x3x3x3x3x3x3x3

(i.e. 4 x 3^7)

[Surferfish]

That's some growth rate BTW.

After 12 hours there would be around 10^86 ants!

That's more than the number of atoms in the universe!

[solimum]

The best way for the child to remember ANY formula is for them to have done the table or similar method themselves outside test conditions, rather than trying to remember by rote something which has no concrete meaning. If they've internalised what's going on, and maybe worked out their own version of the formula, it will be much easier to apply in future.

However I would agree that 4 x(3 to the 7th power) is a bit nasty to calculate in your head anyway - I wouldn't want to have to do that in a hurry!

[streathammum]

Solimum's suggestion is a good way to explain and understand what's going on.

But if you want to save time, once you get the idea there's no real need to make a table showing the number after every 4 minute interval.

You should be able to see that at 16:00, without writing out all the intermediate steps, the total number is 4x3x3x3x3x3x3x3

(i.e. 4 x 3^7)

That is a helpful way of thinking about it. But even assuming you do the first few sums in your head, you're still likely to need to do four of five calculations on paper to find the answer. If it's only worth one point, and other questions also worth one point have got fewer steps, then it's probably worth leaving this one until the end.

[Surferfish]

Thanks for this but this table will take a long time and the tests are only 10 min tests. How can a child work this out within 60-90 seconds? Is there a quicker formula or should they just skip questions like these for the 11+ exams.

Was this question multiple choice? If so what were the options?

There might be a quicker way to determine the answer by eliminating other options. (e.g. the answer would have to be divisible by 3 and 4)