Question Solved1 Answer Problem begins here: A farmer selected a variety of a fast-growing vegetable which matures based on the differential equation dw/dt = 0.1W + 10, where W is the weight (in kilograms) of the available vegetables at time t (in months). An initial number of the vegetable of weight 46 kilograms were planted. How much can be harvested after 4 months? Assume that no vegetable dies. Do not round off intermediate steps. Round off the final answer to two decimal places. For this part of the assessment, choose the correct answer from among the given choices. A 68 kilograms B) 69 kilograms 76 kilograms D 118 kilograms E) 124 kilograms F 134 kilograms G 160 kilograms H) 168 kilograms

T3IZ26 The Asker · Calculus

Transcribed Image Text: Problem begins here: A farmer selected a variety of a fast-growing vegetable which matures based on the differential equation dw/dt = 0.1W + 10, where W is the weight (in kilograms) of the available vegetables at time t (in months). An initial number of the vegetable of weight 46 kilograms were planted. How much can be harvested after 4 months? Assume that no vegetable dies. Do not round off intermediate steps. Round off the final answer to two decimal places. For this part of the assessment, choose the correct answer from among the given choices. A 68 kilograms B) 69 kilograms 76 kilograms D 118 kilograms E) 124 kilograms F 134 kilograms G 160 kilograms H) 168 kilograms
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Transcribed Image Text: Problem begins here: A farmer selected a variety of a fast-growing vegetable which matures based on the differential equation dw/dt = 0.1W + 10, where W is the weight (in kilograms) of the available vegetables at time t (in months). An initial number of the vegetable of weight 46 kilograms were planted. How much can be harvested after 4 months? Assume that no vegetable dies. Do not round off intermediate steps. Round off the final answer to two decimal places. For this part of the assessment, choose the correct answer from among the given choices. A 68 kilograms B) 69 kilograms 76 kilograms D 118 kilograms E) 124 kilograms F 134 kilograms G 160 kilograms H) 168 kilograms
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{:[dw//dt=0.1 w+10],[(dw)/(0.1 w+10)=dt]:}Integrated wr.to toboth the sides{:[int(dw)/(0.1 w+10)=int dt.],[(1)/(0.1)ln(0.1 w+10)=t+c],[10 ln(0.1 omega+10)=t+c],[" at "t=0quad w=46],[10 ln(0.1 xx46+10)=0+c],[c=10 ln(4.6+10)=],[c=10 ln(10+6)],[10 ln(0.1 w+10)-10 ln(14.6)=t] ... See the full answer