UpStudy Free Solution:

The graph shown is a typical representation of an exponential decay function. The general form of an exponential decay function is:

\[y = ae^ { - bx} \]

where \(a\) and \(b\) are positive constants.

In this graph, as \(x\) increases, \(y\) decreases rapidly and approaches zero but never actually reaches zero, which is characteristic of exponential decay.

Therefore, the function shown in the graph is an exponential decay function, such as \(y = e^ { - x} \), \(y = 2e^ { - x} \), or any similar form with different constants.

Supplemental Knowledge

The graph shown appears to be an exponential decay function. Exponential functions have the general form:

\[y = a \cdot b^ x\]

where:

- \(a\) is a constant,

- \(b\) is the base of the exponential (for decay, \(0 < b < 1\)),

- \(x\) is the exponent.

In an exponential decay function, as \(x\) increases, \(y\) decreases rapidly at first and then levels off, approaching zero but never actually reaching it. This behavior matches the graph provided.

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