To find the number of bacteria at 8:00 a.m., we need to work backward from 9:00 a.m. Since the bacteria double every hour, we can set up the following relationship.
Let \( n \) be the number of bacteria at 8:00 a.m.
At 9:00 a.m., there are 120 bacteria. Since the bacteria double every hour, we can write:
\[ n \times 2 = 120 \]
To solve for \( n \), we can divide both sides by 2:
\[ n = \frac{120}{2} = 60 \]
Therefore, at 8:00 a.m., there were 60 bacteria.
The equation representing the number of bacteria at 8:00 a.m. can be expressed as:
\[ n = 120 \times \frac{1}{2}^1 \]
or more generally as:
\[ n = 120 \times 2^{-1} \]
This confirms that at 8:00 a.m., there were indeed 60 bacteria.
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