# A bacteria population is growing exponentially with a growth factor of 1/6 each hour.

A bacteria population is growing exponentially with a growth factor of $\frac{1}{6}$ each hour.By what growth rate factor does the population change each half hour.Select all that apply
a: $\frac{1}{12}$
b: $\sqrt{\frac{1}{6}}$
c: $1/3$
d: $\sqrt{6}$
e: ${\frac{1}{6}}^{\frac{1}{2}}$

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Given:
The bacteria population has an exponential growth with a factor of $\frac{1}{6}$ per hour. The growth factor has to be determined for the population change each half hour.
Step 2
To find the growth factor for every half an hour as follows,
For an exponential function,
Growth factor of one hour = (Growth factor of half an hour)2
Assuming growth factor of half an hour as x,
$\frac{1}{6}={x}^{2}$
$x=\sqrt{\frac{1}{6}}$
$x={\frac{1}{6}}^{\frac{1}{2}}$
Hence the growth factor is ${\frac{1}{6}}^{\frac{1}{2}}$ or $\sqrt{\frac{1}{6}}$