Find the Domain 12e^((-t)/6)=0

Problem

12*e(−t/6)=0

Solution

1. Identify the type of function involved in the expression. The expression 12*e(−t/6) is an exponential function.

2. Determine the constraints for the exponent. The exponent is −t/6 which is a linear polynomial in terms of t

3. Recall the domain of the natural exponential function eu The function eu is defined for all real numbers u

4. Analyze the specific exponent −t/6 Since there are no variables in denominators or under even-indexed roots within the exponent, it is defined for all real values of t

5. Conclude that the domain of the function ƒ(t)=12*e(−t/6) is the set of all real numbers. Note that while the equation 12*e(−t/6)=0 has no solution (since eu>0 for all u, the domain refers to the values of t for which the expression is defined.

Final Answer

Domain: *(−∞,∞)

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