Question

Find the equation of the exponential function represented by the table below:
xx yy
00 33
11 66
22 1212
33 2424

Answer 1

The exponential function represented by this table can be written in the form y = ab^x, where a is the initial value and b is the growth factor.

Looking at the table, we can see that the initial value (when x = 0) is 33, so a = 33.

To find the growth factor, we can look at the ratio of consecutive y-values:

66/33 = 2 (the growth factor here is 2)
1212/66 = 2 (the growth factor here is also 2)
2424/1212 = 2 (the growth factor here is also 2)

Since the growth factor is consistent for all pairs of consecutive y-values, we can conclude that b = 2.

Therefore, the equation of the exponential function represented by this table is y = 33 * 2^x.