Determine whether the function is a power function. If the function is a power function, state the power and constant of variation.
f(x)=5*7^x
it's an exponential function.
To determine whether the function is a power function, we need to examine its form. A power function can be written in the general form:
f(x) = k * x^a
where k is the constant of variation and a is the power.
Now, let's compare this general form to the given function f(x) = 5 * 7^x. We notice that the exponent x is not attached to x in this function, but instead attached to 7. This means that the function is an exponential function, not a power function.
In an exponential function, the variable is the exponent. In this case, the base is 7, and the variable in the exponent is x.
So, to determine the nature of this function, we can analyze its general characteristics. In the function f(x) = 5 * 7^x, the base 7 is constant, and when x increases, the value of the function also increases. Thus, this function is an exponential growth function.
To summarize, the given function f(x) = 5 * 7^x is not a power function but an exponential growth function.