Question

1. given the two exponential functions below, circle the one that represents a geometric sequence. use complete sentences to explain why one is a geometric sequence and the other is not. graph a graph b explanation:

Explanation:

A geometric sequence has a common ratio between consecutive terms. For an exponential - function representing a geometric sequence, when we consider discrete points (usually for integer - valued inputs), the ratio of the function values at consecutive integer points is constant. If we assume the general form of an exponential function \(y = a\cdot b^{x}\), for a geometric sequence, when \(x = n\) and \(x=n + 1\) (\(n\in\mathbb{Z}\)), \(\frac{y(n + 1)}{y(n)}=\frac{a\cdot b^{n+1}}{a\cdot b^{n}}=b\) (constant). We need to check the ratio of \(y\) - values at consecutive integer \(x\) - values on each graph. If the ratio is constant for all consecutive integer \(x\) - values, it represents a geometric sequence.

Answer:

We need the actual \(y\) - values at integer \(x\) - values on Graph A and Graph B to determine which one represents a geometric sequence. Without specific values, we cannot circle the correct graph or provide a definite answer.