## 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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