Germfarm math

**Rambo** · Mar 11th 2008, 02:09 AM

in a germfarm the germs increase exponentically that means after every 20 minutes the germs double in quantity.

a) at 12 oclock the germs are 700. how many are they at 15 oclock?

B) how many where they at 10 oclock?

c)Whats the clock when the germs are 1 000 000?

Thanks again guys need a quick answer, Please the whole calculation not only the answers guys. Im in deep ****.

**colby2152** · Mar 11th 2008, 04:42 AM

Originally Posted by Rambo

in a germfarm the germs increase exponentically that means after every 20 minutes the germs double in quantity.

a) at 12 oclock the germs are 700. how many are they at 15 oclock?

B) how many where they at 10 oclock?

c)Whats the clock when the germs are 1 000 000?

Thanks again guys need a quick answer, Please the whole calculation not only the answers guys. Im in deep ****.

$f(t)=2^{3t} A$

Let t = 0 denote noon/1200/12:00PM

$f(t)=2^{3t} 700$

Plug t = 3 for 1500/3:00PM and t = -2 for 1000/10:00AM

**Rambo** · Mar 11th 2008, 07:23 AM

Originally Posted by colby2152

$f(t)=2^{t/20} A$

Let t = 0 denote noon/1200/12:00PM

$f(t)=2^{t/20} 700$

Plug t = 3 for 1500/3:00PM and t = -2 for 1000/10:00AM

Shouldnt the solution be $f(t)=2^{9} 700 =358400$
because thr population doubles every 20 minutes that means in 3 hours 12-15 it doubles 9 times?
And b) $f(t)=2^{-6} 700= 10,9375$
Becaus 10-12 is 2 and bacwards -2 hours and the germs double 6 times in 2hours?

**colby2152** · Mar 11th 2008, 07:25 AM

Originally Posted by Rambo

Shouldnt the solution be $f(t)=2^{9} 700 =358400$
because thr population doubles every 20 minutes that means in 3 hours 12-15 it doubles 9 times?
And b) $f(t)=2^{-6} 700= 10,9375$
Becaus 10-12 is 2 and bacwards -2 hours and the germs double 6 times in 2hours?

I fixed it up... not sure what I was thinking with the time parameter, but you are right, it should be 3t! Good job pointing that out!

**Rambo** · Mar 11th 2008, 07:31 AM

Originally Posted by colby2152

I fixed it up... not sure what I was thinking with the time parameter, but you are right, it should be 3t! Good job pointing that out!

Thats what i tought too any idea how i should get to know when the germs are 1000 000?

**Tally** · Mar 11th 2008, 08:11 AM

At 15:20 = 716800 germs
At 15:40 = 1433600 germs, so in 20minutes 716800 germs born, divide that by time.

716800/1200=597.333 germs/persec. 1000000-7168000=283200 germs neeeded. So 283200/597.333=474 secs to produce them.

474/60=6mins54secs. So 15:20+6m54secs=

15:26:54 as my answer. Others may see it different, I'm just getting back into things so I hope it helps.

**earboth** · Mar 11th 2008, 08:53 AM

Originally Posted by Rambo

Thats what i tought too any idea how i should get to know when the germs are 1000 000?

With your question the number of germs is calculated by:

$g(t) = 700 \cdot 2^{3t}$ t in hours.

$1,000,000 = 700 \cdot 2^{3t}~\iff~\frac{10000}{7} = 2^{3t}$ . Logarithmize using the ln-function:

$\ln\left(\frac{10000}{7}\right) = 3t \cdot \ln(2)~\iff~ 3t = \frac{\ln\left(\frac{10000}{7}\right)}{\ln(2)}$ and therefore:

$t = \frac{\ln\left(\frac{10000}{7}\right)}{3 \cdot \ln(2)}\approx 3.49345...$ and

$3.49345.. h \approx 3h\ 29 min\ 36.4 s$

**Tally** · Mar 11th 2008, 09:32 AM

^^^^^ Much prettier than mine, and I'm sure more accurate. Nice work earboth.

**CaptainBlack** · Mar 15th 2008, 08:04 AM

Originally Posted by Tally

At 15:20 = 716800 germs
At 15:40 = 1433600 germs, so in 20minutes 716800 germs born, divide that by time.

716800/1200=597.333 germs/persec. 1000000-7168000=283200 germs neeeded. So 283200/597.333=474 secs to produce them.

474/60=6mins54secs. So 15:20+6m54secs=

15:26:54 as my answer. Others may see it different, I'm just getting back into things so I hope it helps.

The number of germs does not increase by the same amount every 20 minutes
but doubles every 20 minutes. This is is results in a very much faster growth in
the population and this is the point of questions like this.

This is exponential growth.

RonL

**Tally** · Mar 15th 2008, 09:41 AM

Ah yes... After 20 years I decide to head back to school to become a high school math teacher. Hope I didn't leave it too late.

Any good sites where I can read up on stuff like this?

**CaptainBlack** · Mar 15th 2008, 10:50 AM

Originally Posted by Tally

Ah yes... After 20 years I decide to head back to school to become a high school math teacher. Hope I didn't leave it too late.

Any good sites where I can read up on stuff like this?

Wikipeadia is very good for maths topics as is mathworld

RonL

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