---- A yeast culture weighing 2 grams is removed from a refrigerator unit and is
ID: 3346394 • Letter: #
Question
----
A yeast culture weighing 2 grams is removed from a refrigerator unit and is expected to grow at the rate of W'(t) = 0.3 e 0.2t grams per hour at a higher controlled temperature. How much will the weight of the culture increase during the first 9 hours of growth? How much will the weight of the culture increase from the end of the 9th hour to the end of the 18th hour of growth? The weight increase during the first 9 hours is approximately grams. (Type an integer or decimal rounded to three decimal places as needed.) The weight increase from the 9th to the 18th hour is approximately grams. (Type an integer or decimal rounded to three decimal places as needed.)Explanation / Answer
w'(t)=0.3(e^0.2t) -(1)
therefore integrating both sides
w(t)=1.5(e^0.2t)+c -(2)
at t=0 w(t)=2 grams
therefore putting t=0 in (2)
2=1.5+c
c=0.5
w(t)=1.5(e^0.2t)+0.5
Weight increase during 1st 9hrs of growth=w(9)-w(0)=[1.5(e^0.2*9)+0.5]-2=7.57 grams
Weight increaes from the 9th to the 18th hr=w(18)-w(9)=[1.5(e^0.2*18)+0.5]-[1.5(e^0.2*9)+0.5]=45.82 grams
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.