Ask Me Help Desk - Applications of exponential/logarithmic functions

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Applications of exponential/logarithmic functions

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

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?

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

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.

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

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

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