3 1 32 2 Points Details This Question Has Several Parts That Must Be Completed Sequentially If You Skip A Part Of Th 1 (62.46 KiB) Viewed 31 times
3. [1.32/2 Points] DETAILS This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. The Pacific halibut fishery has been modeled by the differential equation dy = ky(1 - 1) where y(t) is the biomass (the total mass of the members of the population) Exercise (a) If y(0) = 2 x 107 kg, find the biomass a year later. PREVIOUS ANSWERS SCALCET8 9.4.005.MI.SA. Step 1 The solution to the differential equation = xy(1) has the form y(t) = Step 2 We have been told the carrying capacity is M = 8 x 107 kg and that k = 0.82. Since y(0) = 2 x 107 kg, then we have the following. A = 3 We have y(t) = 8 x 107 1+ 3e 0.82r Rounding to two decimal places, we have the following. y(1) 1.02 x x 107 kg Exercise (b) Submit Skip (you cannot come back) kilograms at time t (measured in years), the carrying capacity estimated to be M = 8 x 107 kg, and k = 0.82 per year. MY NOTES M 1+ Ae-kt with A = M-y(0) y(0) PRACTICE ANOTHER
Step 2 We have y(t) = Rounding to two decimal places, we have the following. y(1) 1.02 x x 107 kg Submit Skip (you cannot come back) 8 x 107 1+ 3e-0.82r Exercise (b) If y(0) = 2 x 107 kg, how long will it take for the biomass to reach 4 x 107 kg? Step 1 We must solve 4 x 107- Step 2 8 x 107 1+ 3e-0.82t Cross-multiplying and dividing gives us the following. 1+ 3e-0.82t2✔ 2 Step 3 Now we have e-0.82t=1/3 ✓ for t. Submit Skip (you cannot come back) 1/3 , and so -0.82t = In Therefore, rounding to two decimal places, we have the following t= 1.28 X yr ✔
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