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✒ [tex]\underline{\underline{\large{\red{\mathcal{GIVEN:}}}}}[/tex]
[tex]\bullet \: \: \rm{1,000 \: bacteria}[/tex]
[tex]\bullet \: \: \rm{8 \: hours}[/tex]
[tex]\underline{\underline{\large{\red{\mathcal{REQUIRED:}}}}}[/tex]
[tex]\underline{\underline{\large{\red{\mathcal{SOLUTION:}}}}}[/tex]
We will use the [tex]\tt{\purple{Geometric \: Sequence}}[/tex] Formula:
[tex]\large{\boxed{\bm{\red{ a_{n} = a_{1}(r {)}^{n - 1} }}}}[/tex]
[tex]\tt{Where;}[/tex]
[tex]\tt{\: a_{1}= 1,000 }[/tex]
[tex]\tt{bacteria \: \: per \: \: hour= \: r= 2 }[/tex]
Let's substitute those term and values:
[tex]\tt{ a_{9} = 1000 \: \cdot \: {2}^{9 - 1} }[/tex]
Simplify:
[tex]\tt{ a_{9} = 1000 \cdot 256}[/tex]
[tex]\large{\boxed{\tt{\purple{a_{9}=256,000}}}}[/tex]
Therefore, the bacteria are in the culture at the end of 8 hours is 256,000.