From the uploaded graph, the curve corresponds to the general exponential form $y = a b^x$. Observing the graph, here are the characteristics:

1. The graph passes through $(0, 1)$, indicating $y = 1$ when $x = 0$. This confirms $a = 1$ (since any $b^0 = 1$).

2. For $x > 0$, $y$ increases rapidly, and for $x < 0$, $y$ approaches zero but remains positive. This indicates $b > 1$, as the function grows exponentially for increasing $x$ and decays (but stays positive) for decreasing $x$.

Possible Values for $b$:

Given the behavior of the graph:

• $b$ must satisfy $b > 1$.
• Common possible values for $b$ include $b = 2, 3, e, 4, 5,$ etc.

If you need further details on solving or verifying specific $b$ values, feel free to ask!

Related Questions:

1. What happens if $b$ is less than 1 in $y = a b^x$?
2. How does changing $a$ affect the graph of $y = a b^x$?
3. How can we confirm the value of $b$ using points on the graph?
4. What is the derivative of $y = a b^x$, and what does it tell us about the rate of change?
5. How does $b$ relate to the growth rate of the exponential function?

Tip:

The base $b$ of the exponential function directly determines the growth factor; doubling $b$ will dramatically increase the steepness of the curve!