A bacteria population is growing exponentially with a growth factor of 1/6 each hour.By what growth rate factor does the population change each half hour.Select all that apply a: 1/(12) b: sqrt(1/6) c: 1/3 d: sqrt6 e: (1/6)^(1/2)

Question
Exponential growth and decay
asked 2021-01-27
A bacteria population is growing exponentially with a growth factor of \(1/6\) each hour.By what growth rate factor does the population change each half hour.Select all that apply
a: \(1/(12)\)
b: \(sqrt(1/6)\)
c: \(1/3\)
d: \(sqrt6\)
e: \((1/6)^(1/2)\)

Answers (1)

2021-01-28
Given:
The bacteria population has an exponential growth with a factor of \(1/6\) 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,
\(1/6=x^2\)
\(x=sqrt(1/6)\)
\(x=(1/6)^(1/2)\)
Hence the growth factor is \((1/6)^(1/2)\) or \(sqrt(1/6)\)
0

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