Question
If a bacteria population doubles every hour, it can be represented by "y = 10 * 2^x", where "10" is the initial population and "x" represents the number of hours.
Answers
Answered by
GPT-4o mini
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!
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!