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: dNdt=rN[(K−N)K]

dN = population size change

dt = time interval

r = (max) growth rate

N = starting population size

K = carrying capacity

So: r=(90+100)/2

r=95/hour

(average between max growth rate between hours 8 and 10)

dN/dt=95N[(K−N)/K]

With N=2

dN/dt=95(2)[(K−2)/K]

and if K value is carrying capacity, K=600

dN/dt=95(2)[(600−2)/600]

dN/dt=190(598/600)

dN/dt=190(0.997)

dN/dt=189?

However, the question asks me to "Write out the mathematical equation it follows." So am I supposed to leave a value unknown or?

Answer 1

Yes! As carrying capacity of the samples reached its maximum by 13hr time period, and the growth rate is not a constant value but caged with time it is considered to be logistic growth modal.

So you are not supposed to determine values, as the data pretty well suited in to the mathematical modal. But in order to support your assumption you need to calculate population growth rate..