Question

The table represents some points on the graph of an exponentialfunction.x-2-1012f(x)12.5 15 18 21.6 25.92 Which function represents the same relationship?A f(x) = 15(5/6)xB f(x) = 18(6/5)xC f(x) = 15(6/5)xD f(x) = 18(5/6)x

Answer 1

Take into account that the general form of an exponential function is:

f(x) = a(r)^x

if r is lower than one the function increases, otherwise the function decreases.

Based on the information of the table, you can identify that the function increases. Then, r > 1. From the given options, 6/5 is a number greater than 1.

To determine what is the value of a, in the general expression, you can use any pair of values of the table, replace in the general form of the function and solve for a, as follow:

12.5 = a(6/5)⁻²

12.5 = a(0.694)

a = 12.5/0.694

a = 18

Hence, the exponential function of the data of the table is:

f(x) = 18(6/5)^x