We want to tell whether the table of values represents a linear, exponential, or quadratic function. To do so, we will analyze how the consecutive terms are related to each other.
Note that the difference between consecutive x-values is always 1 — it is constant.
Additionally, the consecutive y-values have a common ratio of 2. This means that the table represents an exponential function.
Let's recall the general form of this type of function.
y=ab^x
We will use two ordered pairs given in the table to find the values of a and b. For simplicity, let's use (0,8) and (1,16). We will start by substituting 0 and 8 for x and y, respectively.
We can write a partial equation of the function represented by the table.
y=8b^x
To find the value of b we will substitute 1 for x and 16 for y into our partial equation.
