Question

Graph an exponential expression in the form a to the power of x + b so that the exponential equation 2 to the power of x = a to the power of x + b has no solutions.

Answer 1

Graph a^x + b with b > 0 to ensure the graph is always above 2^x, indicating no points of intersection, hence no solutions to the equation.

Step-by-step explanation:

The student is asking about graphing an exponential expression of the form a^x + b such that the equation 2^x = a^x + b has no solutions. To ensure that there are no solutions, we want b to be a positive number, so the graph of a^x + b is always above the graph of 2^x. Since 2^x increases without bound as x increases, if we set b > 0, the graph of a^x + b starts higher and increases at the same rate (if a = 2) or at a faster rate (if a > 2), which ensures that the two graphs never intersect.