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Find the value of t at which the stored energy has 1/e of the value you found in part g

User Villasv
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Final Answer:

The value of
\( t \) at which the stored energy has
\( (1)/(e) \) of the value found in part g is given by
\( t = -(1)/(\lambda) \ln\left((1)/(e)\right) \).

Step-by-step explanation:

In the given question, the stored energy as a function of time
\( t \) is likely expressed using an exponential function involving
\( \lambda \). To find the time at which the stored energy has
\( (1)/(e) \) of its maximum value, we set the expression for stored energy equal to
\( (1)/(e) \) times the maximum value and solve for
\( t \).

The formula
\( t = -(1)/(\lambda) \ln\left((1)/(e)\right) \) is derived from the fact that the natural logarithm of
\( (1)/(e) \) is equal to -1. This time value corresponds to the point in time when the stored energy has decayed to
\( (1)/(e) \) of its maximum value. The negative sign indicates a decay or decrease in energy over time.

It's crucial to understand the mathematical relationship between the exponential function, natural logarithm, and the concept of
\( (1)/(e) \) to interpret and apply the formula correctly in the context of the stored energy function.

User Amin Ghasemi
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