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Bacteria usually reproduce by a process called binary fission. In this type of reproduction, one bacterium divides to

form no bacteria. Under ideal conditions, some bacteria reproduce every 15 minutes.
Find the constant k for this type of bacteria under ideal conditions. Assume t is in minutes.
0.693
-0.954
0.0462
0.133

1 Answer

3 votes

Answer:


\large \boxed{\text{0.0462 min}^(-1)}

Explanation:

One formula for the reproduction of bacteria is


(N)/(N_(0)) = e^(kt)

Data:

N = 2

N₀ = 1

t = 15 min

Calculation:


\begin{array}{rcl}(N)/(N_(0))& =& e^(kt)\\\\(2)/(1)& = & e^{k*15 \text{ min}}\\\\2 & = & e^{15k \text{ min}}\\\ln 2 & = & 15k \text{ min}\\k & = & \frac{\ln2 }{\text{15 min}}\\\\& = & \textbf{0.0462 min}^{\mathbf{-1}}\\\\\end{array}\\\text{The value of the constant k is $\large \boxed{\textbf{0.0462 min }^{\mathbf{-1}}}$}

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