Question

in an experiment with a cell line, 30% of the cells in a petri dish divide into two every hour and 10% of the cells die every hour. The remaining 60% of the cell survive without dividing. Let y_n​ be the number of cells in the petri dish after n hours. Suppose that y0​=100. Determine the correct recursive formula for y_n​ (for all n>0) and use it to compute the value of y2

Answer 1

Deduction of recursive relation:

Suppose there are n number of cells at any instant of time.

• 30 % of n => (30/100) * n = 0.3 * n, After an hour these cells will divide and get doubled therefore it will become 2 * 0.3 * n = 0.6 * n.
• 60 % of n   => (60/100) * n = 0.6 * n, these cells will just survive they will neither die nor divide and the number of these cells will remain 0.6 * n.
• 10 % of n will die.

Hence after 1 hour of time the number of cell = 0.6 * n + 0.6 * n = 1.2 * n.

Therefore recursive relation will be:-

y_n = 1.2 * y_n-1 ....for n>0

y_0 = 100 ....for n=0

Computation of y2:

y_2 = 1.2 * y_1

=> y_2 = 1.2 * 1.2 * y_0

=> y_2 = 1.2 *1.2 * 100 .......using the given value of y_0

=> y_2 = 1.44 * 100

=> y_2 = 144