You are correct! The equation \( y = 10 \times 2^x \) describes the growth of a bacterial population that starts with an initial population of 10 and doubles every hour.
In this equation:
- \( y \) represents the bacterial population at time \( x \), where \( x \) is the number of hours that have passed.
- The base \( 2 \) signifies that the population doubles every hour.
- The coefficient \( 10 \) indicates the initial number of bacteria.
For example, after:
- 1 hour (\( x = 1 \)): \[ y = 10 \times 2^1 = 20 \]
- 2 hours (\( x = 2 \)): \[ y = 10 \times 2^2 = 40 \]
- 3 hours (\( x = 3 \)): \[ y = 10 \times 2^3 = 80 \]
- 4 hours (\( x = 4 \)): \[ y = 10 \times 2^4 = 160 \]
And so on. The population grows exponentially in this manner as time progresses. If you have any further questions about bacterial growth or related topics, feel free to ask!