Final answer:
The exponential function with a growth rate of 0.5% is f(x) = e^0.005x. This is because the growth rate percentage needs to be converted to a decimal, making it 0.005, which is then used as the exponent base e.
Step-by-step explanation:
The exponential function that has a growth rate of 0.5% is f(x) = e^0.005x. The percentage growth rate can be converted into a decimal by dividing by 100, so 0.5% becomes 0.005. The base of the exponential function is the constant e (approximately 2.71828), which is raised to the power of the growth rate multiplied by the variable x. Therefore, as the variable x increases by 1 unit, the function value multiplies by approximately e^0.005 to reflect a 0.5% growth rate. When dealing with exponential growth, the essential feature is the function increasing by a constant percentage over equal time intervals. This is represented by the base e raised to the power of the product of a growth rate and the variable x in the exponential function.