To find the number of bacteria at 8:00 a.m., we need to go back one hour from 9:00 a.m. when the bacteria count was 120. Since the bacteria double every hour, we can represent the number of bacteria at any hour as follows:
Let \( n \) be the number of bacteria at a certain hour. If the amount doubles every hour, we can express the relationship between the number of bacteria at 8:00 a.m. (let's denote it as \( n_0 \)) and the number at 9:00 a.m. as follows:
\[ n = n_0 \times 2^{(t)} \]
where \( t \) is the number of hours that have passed.
From 8:00 a.m. to 9:00 a.m., \( t = 1 \) (one hour has passed). At 9:00 a.m., there are 120 bacteria:
\[ 120 = n_0 \times 2^{1} \]
To find \( n_0 \), we simplify the equation:
\[ 120 = n_0 \times 2 \]
Dividing both sides by 2 gives:
\[ n_0 = \frac{120}{2} = 60 \]
Thus, the equation representing the number of bacteria at 8:00 a.m. is:
\[ n = 60 \times 2^{(1)} \]
And there were 60 bacteria at 8:00 a.m.