Applications of Exponential & Log Function Derivatives

4. The current in a circuit is given by:

i = 4t^{2}e^{8/t}

Find the times when the current is a minimum or maximum.

We need to take the derivative of i with respect to time, set it equal to zero, and solve.

Use the Product Rule:

di/dt =4t^{2}e^{8/t} (-8/t^{2}) + 8te^{8/t}

0 = e^{8/t}[-32 + 8t]

0 = -32 + 8t

t = 4 sec This is a minimum.