Logarithm word problem (don't know much about logs)

[runaway]

Hi can someone please explain how I do the following....Not familiar with logs that much

Formula: Growth rate (k)

k = logN₁ - logN₀ / tlog2

1. A population of Escherichia coli, which increases from 2000 cells to 120 000 cells in 124 minutes during exponential phase. When incubated at 40 degrees.

1.1 Calc. the number of generations per hour? convert minutes to hours.

I am not particular sure how to use these formula, and calc. logs on the calculator.

2.1 Make t the subject of the formula:

g = tlog2 / logN₁ - logN₀
________________________________
Edited by stapel -- Reason for edit: Making subscripts visible.

 

[Deleted member 4993]

Re: Logs

Hi can someone please explain how I do the following....Not familiar with logs that much

Formula: Growth rate (k)

k = logN1 - logN0 / tlog2

1. A population of Escherichia coli, which increases from 2000 cells to 120 000 cells in 124 minutes during exponential phase. When incubated at 40 degrees.

1.1 Calc. the number of generations per hour? convert minutes to hours.

I am not particular sure how to use these formula, and calc. logs on the calculator.

2.1 Make t the subject of the formula:

g = tlog2 / logN1 - logN0

Please review logarithm and its laws at:

http://www.purplemath.com/modules/logs.htm

http://www.purplemath.com/modules/logrules.htm

Then post your work so that we know where to start.

 

[Denis]

Formula: Growth rate (k)
k = logN₁ - logN₀ / tlog2

VERY messy formula; I suggest:
k = growth rate
p = present population
f = future population
t = time
k = log(f) - log(p) / (t log(2))

1. A population of Escherichia coli, which increases from 2000 cells to 120 000 cells in 124 minutes during exponential phase. When incubated at 40 degrees.
1.1 Calc. the number of generations per hour? convert minutes to hours.

I am not particular sure how to use these formula, and calc. logs on the calculator.

If you don't know how to calculate logs on a calculator, what do you expect?
Have you tried entering say "log(2000)" in the google search box?

Anyway, 124 minutes = 31/15 hours: you ok with that?
So we have: log(120000) - log(2000) / [(31/15) log(2)] = ~6.39;
in the same way as .09 = 9%, 6.39 = 639%:
however, that result doesn't seem correct; why is log(2) in your formula:
who gave you that?

The true rate can be calculated this way:
2000(1 + k)^(31/15) = 120000
That'll give you k = ~6.25 or 625%
So trying it out:
2000 * 6.25 = 12500 ; end hour1 = 12500 + 2000 = 14500
14500 * 6.25 = 90625; end hour2 = 14500 + 90625 = 105125
105125(1+6.25)^(1/15) = ~120000 : that's at end of 2 1/15 hours

I have no idea why you're asked to find "generations per hour";
all in all, the whole problem is badly worded!

2.1 Make t the subject of the formula:
g = tlog2 / logN₁ - logN₀

Can you make t the suject here:
a = tx/y - z
If not, you sure need to get back to basics.

 

[runaway]

I have never done logs before, its my first time...I am doing a research project on them, don't have a clue of what is going on

 

[Deleted member 4993]

Did you go to the websites I suggested and read those?

After that - may be Denis's reply will make sense.

Your research project looklike homework problems to me.

 

[runaway]

Could you please tell me if the following working outs are correct..

Formula: Growth rate (k)

k = logN₁ - logN₀ / tlog2

2. A population of Escherichia coli, which increases from 2000 cells to 120 000 cells in 124 minutes during exponential phase. When incubated at 40 degrees.

2.1 Calc. the number of generations per hour? convert minutes to hours.

k = logN₁ - logN₀ / tlog2

N₁ = 120000 N₀ = 2000

t = 2hrs 4min is 2.4

k = log12.10^4 - log2.10^2 / 2.4log2

= 4 - 2 / 2.4log2

= 2,8 generations per hour

3.1 Make t the subject of the formula:

g = tlog2 / logN₁ - logN₀

glogN₁ - logN₀ / log2 = t

 

[Denis]

t = 2hrs 4min is 2.4

NO! 4 min is 4/60 = 1/15 of an hour

4 - 2 / 2.4log2
= 2,8 generations per hour

HOW can that be: log(2) = .69314718..... ??

You really need to have done what Mr Khan suggested, before you even attempt a problem like this one.

Also, review this article or ask someone (teacher, friend...) to show you HOW to post math stuff properly (that is, clearly). For instance, do you know what brackets are for?

Thank you.