Question

Given the exponential function n = 40.25 (1.0394)^t, determine the base of the exponential model and whether it's a growth or decay factor. Option 1: The base is 1.0394; it is a growth factor. Option 2: The base is 1.0394; it is a decay factor. Option 3: The base is 40.25; it is a growth factor. Option 4: The base is 40.25; it is a decay factor.

Answer 1

The base of the given exponential function n = 40.25 (1.0394)^t is 1.0394 and it represents a growth factor as it's larger than 1.

The exponential function given is n = 40.25 (1.0394)^t. In this function, 1.0394 is the base and t is the exponent. The base of an exponential function directly relates to the rate at which the function grows or decays. If the base is larger than 1, the function shows growth, while if the base is less than 1, the function shows decay. Since 1.0394 is larger than 1, it causes the function to grow, not decay. Therefore, in response to your question, the answer is Option 1: The base is 1.0394; it is a growth factor.

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