To solve the problem of determining the number of bacteria in a culture after 7 hours, given that the initial number of bacteria doubles every hour, we use the exponential growth formula:
[tex]\[ N = 12{,}000 \left(2^t\right) \][/tex]
where:
- [tex]\(N\)[/tex] is the number of bacteria after [tex]\(t\)[/tex] hours,
- [tex]\(t\)[/tex] is the time in hours,
- the initial number of bacteria is [tex]\(12{,}000\)[/tex].
For this problem, [tex]\( t = 7 \)[/tex] hours. We need to substitute [tex]\( t = 7 \)[/tex] into the formula and simplify.
Substituting [tex]\( t = 7 \)[/tex] into the formula, we get:
[tex]\[ N = 12{,}000 \left(2^7\right) \][/tex]
First, we calculate [tex]\( 2^7 \)[/tex]:
[tex]\[ 2^7 = 128 \][/tex]
Now, substitute [tex]\( 128 \)[/tex] back into the equation:
[tex]\[ N = 12{,}000 \times 128 \][/tex]
Multiplying these together:
[tex]\[ N = 1{,}536{,}000 \][/tex]
Therefore, the number of bacteria present after 7 hours is [tex]\( 1{,}536{,}000 \)[/tex].
The correct answer is [tex]\( 1{,}536{,}000 \)[/tex].
