Pregunta
A certain type of bacteria decreases according to the model \( P(t)=12,789 \mathrm{e}^{-0.45} t \), where \( P \) is the population of the bacteria after \( t \) minutes. What is the initial population of this sample of bacteria? 11,667 13,678 15,678 12,789
Ask by Rowe Chavez. in the United States
Jan 25,2025
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The initial population of the bacteria is 12,789.
Solución
To find the initial population of the bacteria, we need to evaluate the population function \( P(t) \) at \( t = 0 \).
The population function is given by:
\[
P(t) = 12,789 e^{-0.45t}
\]
Now, let's calculate \( P(0) \):
\[
P(0) = 12,789 e^{-0.45 \cdot 0}
\]
Since \( e^0 = 1 \), we have:
\[
P(0) = 12,789 \cdot 1 = 12,789
\]
Thus, the initial population of this sample of bacteria is \( 12,789 \).
The correct answer is \( 12,789 \).
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Simplifique esta solución Mind Expander
To find the initial population of the bacteria, we need to evaluate the function \( P(t) \) at \( t = 0 \). When we substitute \( t = 0 \) into the equation: \[ P(0) = 12,789 \mathrm{e}^{-0.45 \cdot 0} = 12,789 \mathrm{e}^{0} = 12,789 \times 1 = 12,789. \] So, the initial population of this sample of bacteria is 12,789. Now you know what the bacteria are starting with – they’re ready to take on the world! Not bad for such tiny organisms!
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