4. 2 points Despite loving my little monster of a sourdough culture, I occasiona

Question

4. 2 points Despite loving my little monster of a sourdough culture, I occasionally want to vacation. With an initial population size of 500g, a single feeding will let the population increase by 50% after one day. This feeding also provides sufficient food to let my sourdough starter grow to a size of 2000g. Once it reaches 2000g, the population has consumed all the food and starts dying, and I lose a third of the existing population each day. If I feed my 500g population as I leave for vacation, how long can I be away before the culture reaches back to 500g?

Explanation / Answer

After t days, polpulation = 500(1.5)t

Let after x days, population becomes 2000 gm

2000 = 500(1.5)x

4 = 1.5x

x = log4/ log1.5 = 3.42 days

Now population start decreasing

And the equation is

A = 2000(1- 1/3)t= 2000(2/3)t

500 = 2000(2/3)t

1/4 = (2/3)t

log(1/4)/og(2/3) =t

t=3.42 days

Total time = 3.42+3.42 = 6.84 days

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