Answer:
2,048,000.
Step-by-step explanation:
a. Let the initial number of bacteria = x
Since bacteria doubles every 2 hours, so the sequence will be in the form of
x, 2x, 4x, 8x, .........
This sequence is a geometric sequence with a common ratio of 2.
b. Since explicit formula for a geometric sequence is
[tex]P_{n} =P_{0}(r)^{n}[/tex]
Where, [tex]P_{n}[/tex] = population of bacteria after n hours.
[tex]P_{0}[/tex] = Initial population
r = common ratio
n = number of times population got doubled
By putting the values of each term in the formula :
[tex]P_{24} =500(2)^{12}[/tex]
= [tex]500\times 4096[/tex]
= 2,048,000
After 24 hours population of bacteria would be 2,048,000.
