# Math Help - Bacteria growth!

1. ## Bacteria growth!

My tutor is growing bacteria. She starting off with a mass of 150 grams of bacteria at 12 pm on tuesday, than every hour the mass of bacteria is growing by 15%, but my tutor wants to end up with 3 grams of bacteria.

Should I use a computer or calculator on my level of precision and why should I use it, and using the appropriate device how long will it take for the mass of bacteria to reach 3 grams, and waht is the exact date and time. I am having some serious trouble with this! thankyou

2. ## Re: Bacteria growth!

If you start with 150 grams and it grows by 15% per hour, it's going to get bigger and bigger and will never shrink to 3 grams, so I think you may have used the wrong values. In general the amount of bacteris is :

$A(t) = A_0 (1+i)^n$

where $A_0$ is the starting amount, 'i' is the growth rate per period, and 'n' is the number of periods. If you start with 150 grams and it grows 15% per hour then after 8 hours you have [tex[ 150(1+0.15)^8 = 458.8 grams.

For the inverse problem, if you are given a value for 'A' and want to figure out how many periods it takes to grow to that amount you can rearrange the above formula:

$n = \frac {\log(A/A_0)}{log(1+i)}$

It doesn't matter what base you use for the logarithm - could be log base 10 or natural logs, whatever you prefer, just be consistent. For example to grow from 150 to 1000 grams takes:

$n = \frac {\log(A/A_0)}{log(1+i)} = \frac {\log(1000/150)}{\log(1.15)} = 13.6$ hours.

3. ## Re: Bacteria growth!

Thankyou very much sir... my mistake it was 150 micrograms so I convert that to grams than I calculate it right?
Oh and do you think from your perception that computer or calculator would be the best way to calculate this according to accuracy,,, because it's bacteria??

4. ## Re: Bacteria growth!

Thankyou very much sir... my mistake it was 150 micrograms so I convert that to grams than I calculate it right?
You're welcome, and yes - you must use consistenet units, so if you like you can convert 150 micrograms to 0.000150 grams. Alternatively you could keep everything in units of micrograms, so that the initial 150 micrograms grows to 3 million micrograms.

Oh and do you think from your perception that computer or calculator would be the best way to calculate this according to accuracy,,,
a calculator should work fine, as long as it can calculate logs.