Find the Domain

Problem

P(11)=5000*e^ln(14/5)/8^11

Solution

1. Identify the type of function provided. The expression P(11) is a specific value of an exponential function P(t)=5000*e^(k*t) where t=11

2. Analyze the components of the expression for potential restrictions. The expression contains an exponential function e^u and a natural logarithm ln(x)

3. Check the argument of the natural logarithm. The argument is 14/5 which is a positive constant. Since 14/5>0 the logarithm is defined.

4. Check the exponent for division by zero. The denominator in the exponent is 8^11 which is a non-zero constant.

5. Determine the domain of the underlying function P(t) Exponential functions of the form a⋅e^ƒ(t) are defined for all real numbers t as long as ƒ(t) is defined. Since ƒ(t)=ln(14/5)/8^t (assuming the task implies a general function) or simply a constant value in this specific case, there are no values of t that make the expression undefined.

6. Conclude that the domain of the function P(t) is all real numbers.

Final Answer

Domain=(−∞,∞)

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