Answer:
Number of bacteria after 100 days is 1237.
Step-by-step explanation:
Since bacterial growth is a geometrical sequence.
Therefore, their population after time t will be represented by the expression
[tex]S_{n}=\frac{a(r^{n}-1)}{r-1}[/tex]
Where a = first term of the sequence
r = common ratio of the sequence
n = duration or time
Since first term of the sequence = number of bacteria in the start = 1
Common ratio = r = (1 + 0.04) = 1.04
[tex]S_{100}=\frac{1[(1.04)^{100}-1)]}{1.04-1}[/tex]
= [tex]\frac{(50.5049-1)}{(0.04)}[/tex]
= 1237.64 ≈ 1237 [Since bacteria can't be in fractions]
Therefore, number of bacteria after 100 days is 1237.
