Find the Domain y=10(3)^x

Problem

y=10*(3)x

Solution

1. Identify the type of function. The given equation y=10*(3)x is an exponential function of the form y=a⋅bx where a=10 and b=3

2. Determine the constraints on the input variable x In an exponential function where the base b is a positive constant (b>0, the exponent x can be any real number.

3. Evaluate for any potential restrictions such as division by zero or square roots of negative numbers. Since there are no denominators or radicals involving x there are no restrictions on the domain.

4. Conclude that the domain consists of all real numbers, which can be expressed in interval notation.

Final Answer

Domain:(−∞,∞)

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