# 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
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: $$(1/6)^(1/2)$$

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 $$sqrt(1/6)$$

### Relevant Questions

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1.What is the 5-hour growth/decay factor for the number of mg of caffeine in Diego's body?
2.What is the 1-hour growth/decay factor for the number of mg of caffeine in Diego's body?
3.If there were 180 mg of caffeine in Diego's body 1.49 hours after consuming the energy drink, how many mg of caffeine is in Diego's body 2.49 hours after consuming the energy drink?
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What is the 5-hour growth/decay factor for the number of mg of caffeine in Joseph's body?
What is the 1-hour growth/decay factor for the number of mg of caffeine in Joseph's body?
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Time t (in hours)012345678 Population P(t)501002004008001,6003,2006,40012,800
a. Complete another row of the table with values log (population) and identify the familiar function pattern illustrated by values in that row.
b. Use your calculator to find log 2 and see how that value relates to the pattern you found in the log P(t) row of the data table.
c. Suppose that you had a different set of experimental data that you suspected was an example of exponential growth or decay, and you produced a similar “third row” with values equal to the logarithms of the population data.
How could you use the pattern in that “third row” to figure out the actual rule for the exponential growth or decay model?
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