Help me solve .....How long will it take the colony of 15,000 cells to grow to 250,000 cells?

Question

during its exponential growth phase, a colony of the bacterium E. Coli grew from 15,000 cells to 60,000 cells in 40 minutes. How long will it take the colony of 15,000 cells to grow to 250,000 cells? 

Answer 1

Exponential growth has the formula P = P₀ * e^r*t, where P₀ is the initial population and r is the constant rate of growth.

 

This is the same as ln(P/P₀) = r * t => r = ln(P/P₀)/t, when the log of the both sides of the equation is taken.

 

Using the initial values of P₀ = 15000 and at time t = 40 minutes the population is P = 60000,

 

then r = ln(60000/15000)/40 = ln(4)/40 = ln(2)/20

 

∴ P = 15000e^ln(2)t/20, or when the log of both sides is taken

 

   ln(P/15000) = ln(2)t/20 => t =20 * ln(P/15000)/ln(2)

 

From this, the population will be P = 250000 in t = 20 * ln(50/3)/ln(2) = 81,2 minutes

Answer 2

With all due respect to Sierra, E. coli doubles its population in about 20 minutes. That fact is supported by the given data.

start     20minutes     40minutes     60minutes     80minutes     100minutes

15k          30k               60k              120k             240k           480k

 

So, the number of 250k will be reached in about 85 minutes.

 

Bacterial growth is an exponential function, and the formula is Future value = Present • e^rt

where e ≅ 2.71828, r = rate, and t = time

Answer 3

If it takes 40 minutes for 60,000 cells, then it takes 40 mins for each 45,000 cells to grow. Using that, it would take about 1 mintue for every 1125 cells to grow.  Taking 250000-15000= 235000.  235,000cells÷1125cells/minute= ~209 minutes.