Question

What is the domain and range of the equation y=500(1.08)^x

Answer 1

The domain of y=500(1.08)^x is all real numbers, but may be contextually restricted, while the range is all positive real numbers, as exponential growth functions do not produce non-positive values.

Step-by-step explanation:

The equation y = 500(1.08)^x describes an exponential function where 'y' is the dependent variable and 'x' represents the independent variable, often time. The domain of an exponential function is all real numbers, which means for this function, x can be any real number. However, in practical situations, the domain may be restricted based on context, like in the provided example where x values are from 1981 to 2002. In contrast, the range of an exponential growth function is restricted to positive values because the base of the exponent (1.08) is greater than one, and the coefficient (500) is positive. Therefore, the range is all y > 0, since an exponential growth function never reaches zero and does not produce negative values.

Answer 2

(x) is an element of a real number. This means it could be an integer, fraction or irrational number.

* As x approaches infinity, y approaches infinity.

* As x approaches minus infinity, y approaches 0.

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Domain:

(x) is an element of a real number

Range:

y>0