SOLUTION: The volume of water, v million cubic meters in a lake t ours after a storm is modelled by V = 2t(e^-t)+5 a. What is the initial volume of the lake and he maximum volume of the l

Question 1192700: The volume of water, v million cubic meters in a lake t ours after a storm is modelled by V = 2t(e^-t)+5
a. What is the initial volume of the lake and he maximum volume of the lake.
b. When is the lake emptying the fastest.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
The volume of water, v million cubic meters in a lake t ours after a storm is modelled by V = 2t(e^-t)+5
a. What is the initial volume of the lake and he maximum volume of the lake.
b. When is the lake emptying the fastest.
------------
V(t) = 2t(e^-t)+5
V(0) = 2*0 + 5 = 5 million cubic meters.
------------
Find the 1st derivative:
V'(t) = 2(e^-t) - 2t*e(^-t)
Find the max of V'(t)
V'(t) = 2(e^-t) - 2t*e(^-t) = 0
2e^-t = 2t*e^-t
t = 1 hour

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