Find the Domain N=300/(5+24e^(-0.2t))

Problem

N=300/(5+24*e(−0.2*t))

Solution

1. Identify the potential restrictions for the function. For a rational function, the denominator must not equal zero.

5+24*e(−0.2*t)≠0

2. Analyze the exponential term e(−0.2*t) The range of the natural exponential function eu is always (0,∞)

e(−0.2*t)>0

3. Determine if the denominator can ever be zero. Since e(−0.2*t) is always positive, multiplying it by 24 and adding 5 results in a value that is always greater than 5

5+24*e(−0.2*t)>5

4. Conclude that because the denominator is never zero and the exponential function is defined for all real numbers, there are no restrictions on the input variable t

t∈(−∞,∞)

Final Answer

Domain=(−∞,∞)

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