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sim0nz12345 · Aug 3, 2007, 04:20 AM

Hi there could you please help me with this question

The population of bees in a bee-hive after (n) days is given by P(n)=5000 x 3^(n/40).Find

a) how long it takes for the population to treble,
b) how lone it will take for the population to increase by 20%

Thanks

Capuchin · Aug 3, 2007, 04:30 AM

First we work out what the population is at day 0, plugging 0 in for n we find P(0) is 5000. Now we can set up our equations:

a) solve $5000*3^{\frac{n}{40}} = 5000*3$
b) solve $5000*3^{\frac{n}{40}} = 5000*1.2$

Do you need help solving these?

sim0nz12345 · Aug 3, 2007, 06:09 AM

Yes please
It would be much appreciated if you could show me ow to solve it
Thanks

Capuchin · Aug 3, 2007, 08:57 AM

ill show you the first one.

cancel 5000 from both sides and we have:

$3^{\frac{n}{40}} = 3$

Take ln of both sides:

$ln(3^{\frac{n}{40}}) = ln(3)$

Apply basic log rule $ln(x^a) = aln(x)$ :

$\frac{n}{40}ln(3) = ln(3)$

cancel ln(3) from both sides:

$\frac{n}{40} = 1$

n = 40.

Now you try the next one.

sim0nz12345 · Aug 3, 2007, 05:32 PM

Cool thanks
But why is it 1.2 in b), was it formed from the 20%

Capuchin · Aug 4, 2007, 12:21 AM

Yup 0.2 is the 20% but you want to keep the 100% that you have already so it's 1.2