find the equation of the exponential function represented by the table below:\nanswer attempt 1 out of 2\ny =

Explanation:

Step1: Recall the general form of an exponential function

The general form of an exponential function is (y = ab^{x}), where (a) is the initial value (when (x = 0)) and (b) is the base. When (x = 0), (y=0.01). Substituting (x = 0) into (y = ab^{x}), we get (y=a\times b^{0}). Since (b^{0}=1) for (b\neq0), then (a = 0.01). So the function is (y=0.01b^{x}).

Step2: Find the base (b)

Use the point ((x = 1,y = 0.02)). Substitute (x = 1), (y = 0.02) and (a=0.01) into (y = ab^{x}). We have (0.02=0.01\times b^{1}). Solving for (b), we divide both sides by (0.01): (\frac{0.02}{0.01}=b), so (b = 2).

Answer:

(y=0.01\times2^{x})