find the equation of the exponential function represented by the table below:\nanswer\n

Explanation:

Step1: Recall the general form of an exponential function

The general form of an exponential function is (y = a\cdot b^{x}), where (a) is the initial value ((x = 0)) and (b) is the base. When (x = 0), (y=a\cdot b^{0}=a). From the table, when (x = 0), (y = 1), so (a = 1).

Step2: Find the base (b)

Substitute (a = 1) and the point ((x = 1,y = 4)) into (y=a\cdot b^{x}). We get (y=1\cdot b^{x}), and when (x = 1), (4=b^{1}), so (b = 4).

Step3: Write the exponential function

Substitute (a = 1) and (b = 4) into (y=a\cdot b^{x}). The function is (y = 1\cdot4^{x}=4^{x}).

Answer:

(y = 4^{x})