A culture of a certain bacteria doubles every hour. At 9:00 a.m, there were already 120 bacteria. Which equation represents the number of bacteria, n

, at 8:00 a.m? How many bacteria were there?

1 answer

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.