3. 2 points As an amateur baker, I am growing my own sourdough culture. Like any
ID: 2884423 • Letter: 3
Question
3. 2 points As an amateur baker, I am growing my own sourdough culture. Like any good culture, my culture grows exponentially when I feed it properly. Starting with two separate cultures of size 200g and 300g respectively, I notice that a culture of size 200g takes 1 day to reach 500g after feeding it, and the culture of size 300g takes three quarters of a day to reach 500g after I feed it the same amount. I will harvest the cultures once they reach 2000g. Using an exponential model, find the time required for each culture to reach this harvestable amount. Which grew to 2000g faster? Did this match your expectations?Explanation / Answer
For the first culture
A0 = 200
At (after 1 day) = 500
Using exponential model
A(t) = A0 * e^(kt)
500 = 200 * e^(k * 1)
k = ln(2.5)
Time taken to reach 2000
2000 = 200 * e^(ln(2.5) * t)
ln(10) = ln(2.5) * t
t = 2.51 days
For the second culture
B0 = 300
Bt (after 0.75 day) = 500
Using exponential model
B(t) = B0 * e^(kbt)
500 = 300* e^(kb * 0.75)
k = 4/3 * ln(5/3) = 0.681
Time taken to reach 2000
2000 = 300* e^(0.681 * t)
ln(20/3) = 0.681 * t
t = 2.785 days
Hence the first culture will grow faster to 2000g
Yes, it match our expectations since the growth rate is higher for the first culture as compared to second culture
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