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2 years ago

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A yeast culture weighing 2 grams is removed from a refrigerator unit and is expected to grow at the rate of Upper W prime (t )eq

uals0.1 e Superscript 0.1 t grams per hour at a higher controlled temperature. How much will the weight of the culture increase during the first 10 hours of growth? How much will the weight of the culture increase from the end of the 10th hour to the end of the 20th hour of growth?

1 answer:

Naily [24]2 years ago

5 0

Answer:

a) during the first 10 hours of growth the weight will increase 271.8% relative to the initial state ( or 2.718 g)

b) during the first 20 hours of growth the weight will increase 467.1 % relative to the initial state ( or 4.671 g)

Step-by-step explanation:

since the growing rate law is

W'(t) = 0.1 gr/hour * e^(0.1gr/hour* t) , W'(t) [gr/hour]

and following mathematical conventions: W'(t)= dW/dt

then

dW/dt=0.1 e^(0.1t)

∫dW =∫0.1 e^(0.1t) dt

W = e^(0.1t) + C

at the beginning, (time t=0) the weight is W=2 grams .Therefore

2 g = e^(0.1 g/h*0) + C → 2 g = 1 g + C → C = 1 g

then

W = e^(0.1t) + 1 g

at t= 10 hours

W = e^(0.1 g/h*10h) + 1 g = 3.718 g/h

therefore the weight will increase

ΔW = 3.718 g - 1 g = 2.718 g or 271.8% relative to the initial state

for t=20 hours

W = e^(0.1 g/h*20h) + 1 g = 8.389 g/h

thus, the from t= 10 hours to t= 20 hours the weight will increase

ΔW = 8.389 g/h - 3.718 g = 4.671 g or 467.1 %relative to the initial state

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