Algebra-2

To determine the equation of the exponential function that fits the given table, we can analyze the points provided. The key points on the table are:

(0, 1)

(1, 0.6)

(2, 0.36)

(3, 0.216)

 

The general form of an exponential function is , where a is the initial value and b is the base.

 

Notice the relationship between consecutive y-values:

From (0, 1) to (1, 0.6), y goes from 1 to 0.6.

From (1, 0.6) to (2, 0.36), y goes from 0.6 to 0.36.

From (2, 0.36) to (3, 0.216), y goes from 0.36 to 0.216.

 

This consistent multiplication by 0.6 suggests that b=0.6.

 

Since (0, 1) is on the graph, substituting x = 0 and y = 1 into the equation gives:

Click "Show Answer" to reveal the answer and analysis