Answer to Question #208434 in Algebra for Areeba

Question

Give a practical example of the studied mathematics topics in your particular fields (Biotechnology/Genetics/Microbiology). Example: Geometric sequence It is possible to predict the number of cells in a population when they split by binary fission (The most common mechanism of cell replication in bacteria) at a constant rate. As an example, consider what happens if a single cell divides every 30 minutes for 24 hours. Starting from two cells, the following table shows the increase in cell numbers for the first three generations.

No. of generations No. of Cells

1 2

2 4

3 8

Hence, the number of cells forms a geometric sequence 2, 4, 8, . . . and with a1 = 2 and r = 2, we can find its general term as follows: an = a1r n−1 an = 2(2)n−1 an = 2n Using this general term, we can find number of cells given any number of generation.

Answer 1

(a)

- Differential equations - these are applied in the discussion of evolution of quantitative traits in plants and animal breeding.

- Loci - Loci is applied when there is a selection that acts on diploid locus at which the arbitrary number of alleles can be gotten.

- Algebra - In genetics, the laws of inheritance are encoded as algebraic properties.

(b)

24 hours=1440 minutes

$\frac{1440}{30}=48$

This implies that the cell differentiates 48 times.

(c)

$a_1=2 and r=2$

$a_n=a_1r^{n-1}$

$a_n=2\cdot 2^{n-1}$

$a_n= 2^n$ - this is the general term given in the question.

$a_1=2^1=2$

$a_2=2^2=4$

$a_3=2^3=8$

$a_4=2^4= 16$