To model the growth of bacteria over time, we can use the exponential growth model, which is commonly expressed in the form:
\[ y = y_0 \cdot e^{kt} \]
Where:
- \( y \) is the number of bacteria at time \( t \).
- \( y_0 \) is the initial number of bacteria (at time \( t = 0 \)).
- \( k \) is the growth rate constant (how quickly the bacteria grow).
- \( e \) is the base of the natural logarithm (approximately equal to 2.71828).
- \( t \) is the time (in seconds, in this case).
Example:
Suppose the initial number of bacteria is \( 100 \), and the growth rate constant \( k \) is \( 0.1 \) (which you can adjust based on experimental data). The function would then be:
\[ y = 100 \cdot e^{0.1x} \]
This equation models the number of bacteria \( y \) as a function of time \( x \) in seconds, where you can substitute \( x \) with the desired time to find the corresponding number of bacteria. Adjust \( y_0 \) and \( k \) based on your specific situation to get more accurate modeling.
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