Mammalian cells exhibit a relatively fast growth rate we...

Mammalian cells exhibit a relatively fast growth rate. We observed that mammalian cells, normally triplicate their initial population in 60 hours at 310 Kelvin during the exponential growth phase. (ASSUME GROWTH MODEL) What’s the specific growth rate for these cells under mentioned conditions? What’s the doubling time for these cells? If a population of 1*10^6 cells is required in 120 hours from now, What’s the quantity of cells that you need from now to achieve this?

Transcript

00:01 For the first question here, the exponential growth rate, this rate has the formula that is pt is equal to p0 e to the power k t.

00:21 Here, p t is the population size at time t.

00:33 P0 is the initial population.

00:40 K is the specific growth rate and t here here is the time.

00:54 Now in the first question here it is said that the initial population, let's assume that the initial population that is p0 is equal to n.

01:06 So it is said that p t here will be 3n and time t is equal to 60 hours.

01:16 So if we put this value in the formula then here three, three, three, n is equal to n into e to the power k into 60.

01:26 Here we have to calculate the value of k.

01:29 So here it is e to the power 60 into k is equal to 3 or 60 into k is equal to log of 3 or k is equal to log of 3 divided by 60.

01:48 The value of log 3 is equal to 1 .098 divided by 60, that is equal to 0 .0183.

02:01 This here is our specific growth rate and our first answer.

02:06 Now for the second question, it is said that p t is equal to 2n, that is for the doubling time.

02:18 Here it is the doubling of the population and p0 will be n now we have to calculate the time that is t and specific growth rate k will be 0 .018 3 so here it is the formula is p t is equal to p 0 into 8 e to the power k t so here it is 2n is equal to n into e to the power 0 .0183 into t so it is e to the power 0 .0183 into t is equal to 2 or 0 .183 into t is equal to 2 or 0 .0183 into t is equal to 2 or 0 .0183 into t is equal to log of 2...

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