Final answer:
To determine the exponential function from two points, we need to find the equation of the form f(x) = ab^x, where a and b are constants. We can confirm that all four given equations are already in the form of an exponential function with the base being e (approximately 2.7183) and the constant values provided.
Step-by-step explanation:
Exponential Functions
To determine the exponential function from two points, we need to find the equation of the form f(x) = ab^x, where a and b are constants. Let's consider the given options:
f(x) = e^2x: This is already in the form of an exponential function with a base of e (approximately 2.7183) and a constant of 2. Therefore, the exponential function from these two points is f(x) = e^2x.
f(x) = e^x: Similarly, this is in the form of an exponential function with a base of e and a constant of 1. So, the exponential function from these two points is f(x) = e^x.
f(x) = e^3x: Once again, this is an exponential function with a base of e and a constant of 3. Thus, the exponential function from these two points is f(x) = e^3x.
f(x) = e^4x: Again, this is an exponential function in the form f(x) = ab^x. Here, the base is e and the constant is 4. Therefore, the exponential function from these two points is f(x) = e^4x.