The number of bacteria in the colony after 16 hours = 992
Explanation:The bacteria doubles every 4 hours and we are considering 16 hours
The number of times that the bacteria doubles is 16/4 = 4 times
Note that there is a first term and four other terms when the bacteria were doubled
There are 5 terms in total
Number of terms, n = 5
The initial amount of bacteria, a = 32
The bacteria doubles every 4 hours
That is, the common ratio, r = 2
Since there is a common ratio, this is a geometric progression.
The sum of n terms of a geometric progression is given as:
[tex]S_n=\frac{a(r^n-1)}{r-1}[/tex]Substitute a = 32, r = 2, and n = 5 into the formula above to get the number of bacteria in the colony after 16 hours
[tex]\begin{gathered} S_4=\frac{32(2^5-1)}{2-1} \\ S_4=\frac{32(32-1)}{1} \\ S_4=32(31) \\ S_4=992 \end{gathered}[/tex]The number of bacteria = 992
