Answer:
18.38 × 10⁸.
Explanation:
Cell absorbance is directly proportional to their density
A\alpha cells/mL
A=K ×cells/mL ( Here, K is a constant)
Thus, A/ (cells/mL)=K
Hence, A1/( cells/mL)1=A2/ ( cells/mL)2
Where A1 represents initial absorbance, (cells/mL)1= initial concentration, (cells/mL)2= final concentration, A2= final absorption
Therefore, ( cells/mL)2=(A2* (cells/mL)1 ) / A1
= (1.25 × 5.75 ×10⁶)/1
= 7.18 ×10⁶.
Consequently, the final bacterial concentration in the culture with an absorbance of 1.25 = 7.18 ×10⁶.
Thus, after 8 generations
The growth of cells is geometric, meaning the cell count doubles with each generation, resulting in quadrupling the initial amount after the second generation.
The nth term of geometric progression is expressed as arⁿ⁻¹
where a is the first term, r =2 ( r=nth term/ (n-1) th term)
where n=9 ( n= number of generations+1)
The 9th term therefore becomes (7.18 ×10⁶ × 2⁸)
= 18.38 × 10⁸.
As a result, the number of cells in 1 mL after 8 generations is 18.38 × 10⁸.
Thus, the solution is 18.38 × 10⁸.
