## How do I determine this logistic growth model formula?

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### How do I determine this logistic growth model formula?

**The Question**

Two yeast cells were placed into a special container to which food was continually added, to keep it at a constant concentration. All other factors were set for optimal yeast growth (for example, temperature, oxygen, and pH). The population was sampled every hour for 21 hours and the results of the estimated population size were recorded in the table below.

Time (hour), Number of yeast cells

(0, 2)

(1, 10)

(2, 15)

(3, 20)

(4, 40)

(5, 60)

(6, 100)

(7, 190)

(8, 260)

(9, 350)

(10, 450)

(11, 530)

(12, 580)

(13, 600)

(14, 600)

(15, 600)

(16, 600)

(17, 600)

(18, 600)

(19, 600)

(20, 600)

What population growth model does the population appear to follow? Write out the mathematical equation it follows.

**The Attempt**

Looking at the values, I recognize the carrying capacity is reached at hour 13 with 600 cells, signifying a logistic growth model. The formula given to me for logistic growth is:

dN/dt = rN[(K - N)/K]

From what I have researched:

dN = population size change

dt = time interval

r = growth rate

N = starting population size

K = carrying capacity

So:

dN = 600 - 2 = 598?

dt = 21 hours

r = ?

N = 2

K = 600

Plugging the values in gives me:

598/21 = r2[(600 - 2)/600]

And I have no idea what I'm supposed to do from here.

Do I solve for r? What is the completed formula supposed to look like? There is not sufficient explanation from the teacher's lesson and I don't understand other examples online.

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