State whether the equation y=10^3x represents a linear, quadratic, or exponential function. Tell how you decided.
I think it is exponential
it is an exponential function. Notice the power to x. e^x,2^x...are all expontential functions.
I thought so, just wanted to verify. Thank you
You are correct! The equation y = 10^3x represents an exponential function.
To determine the type of function, you can observe the form of the equation. In this case, we have y = 10^3x, which can also be written as y = (10^3)^x.
Exponential functions usually have a constant base raised to a variable power. In this equation, the base is 10 raised to the power of 3x. The exponent, 3x, depends on the input variable x.
In contrast, linear functions have a constant rate of change, and their equations typically involve a coefficient multiplied by x but not raised to a power. Quadratic functions involve x squared or higher powers of x.
Since our equation involves a constant base (10) raised to a variable power (3x), it fits the definition of an exponential function.