Questions: Classify the function as linear, quadratic, or exponential. f(x)=677(1.226^x)

Solution Steps

To classify the function \( f(x) = 677 \left(1.226^x\right) \), we need to identify its form. A linear function has the form \( f(x) = mx + b \), a quadratic function has the form \( f(x) = ax^2 + bx + c \), and an exponential function has the form \( f(x) = a \cdot b^x \). The given function matches the form of an exponential function.

The given function is \( f(x) = 677 \left(1.226^x\right) \). To classify this function, we compare its form with the standard forms of functions: linear, quadratic, and exponential.

• A linear function has the form \( f(x) = mx + b \).
• A quadratic function has the form \( f(x) = ax^2 + bx + c \).
• An exponential function has the form \( f(x) = a \cdot b^x \).

The function \( f(x) = 677 \left(1.226^x\right) \) matches the form of an exponential function, where \( a = 677 \) and \( b = 1.226 \).

Since the function fits the criteria for an exponential function, we conclude that it is classified as such.

Final Answer