Question

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

Answer 1

Answer:

$\large \boxed{\text{0.0462 min}^{-1}}$

Step-by-step explanation:

One formula for the reproduction of bacteria is

$\dfrac{N}{N_{0}} = e^{kt}$

Data:

N = 2

N₀ = 1

  t = 15 min

Calculation:

$\begin{array}{rcl}\dfrac{N}{N_{0}}& =& e^{kt}\\\\\dfrac{2}{1}& = & e^{k\times15 \text{ min}}\\\\2 & = & e^{15k \text{ min}}\\\ln 2 & = & 15k \text{ min}\\k & = & \dfrac{\ln2 }{\text{15 min}}\\\\& = & \textbf{0.0462 min}^{\mathbf{-1}}\\\\\end{array}\\\text{The value of the constant k is \large \boxed{\textbf{0.0462 min }^{\mathbf{-1}}} }$