Question
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
Real Tutor Solution
Tutor-Verified Answer
Answer
The initial population of the bacteria is 12,789.
Solution
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 \( 12,789 \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution 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!
