Math Problem Statement
an oil tank contains some oil. the oil is leaking from the tank. it is found that the volume of oil V (in cm3) in the tank can be estimated by v=32(3+e^(1/5t))^(-1). and t(t>=0) is the number of hours elasped since the leaking begins. find the value of V when dV/dT attains its least value
Solution
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Math Problem Analysis
Mathematical Concepts
Differentiation
Exponential Decay
Optimization
Formulas
V(t) = 32(3 + e^(1/5t))^(-1)
dV/dt = -32/5 * (e^(1/5t) / (3 + e^(1/5t))^2)
Theorems
Chain Rule
Quotient Rule
Critical Points
Suitable Grade Level
Grades 11-12
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