Question

Write an equation for the exponential function represented in the table and graph below.

Answer 1

Given:

Given that the values of x and y in the table.

We need to determine the equation for the exponential function represented in the table and graph the equation.

Equation for the exponential function:

The general equation for the exponential function is given by

$y=a(b)^x$  ------- (1)

Substituting the coordinate (0,6) in equation (1), we get;

$6=a(b)^0$

$6=a$

Thus, the value of a is 6.

Substituting a = 6 in equation (1), we have;

$y=6(b)^x$ -------- (2)

Substituting the coordinate (1,12) in equation (2), we get;

$12=6(b)^1$

$12=6b$

 $2=b$

Thus, the value of b is 2.

Substituting b = 2 in equation (2), we get;

$y=6(2)^x$

Thus, the equation for the exponential function is $y=6(2)^x$

The image of the graph of the exponential function is attached below: