This question involves identifying the possible values for $b$ in the exponential function $y = a(b)^x$, based on the graph provided.

From the graph, the following observations can be made:

1. The graph represents exponential growth, which is indicated by the fact that as $x$ increases, $y$ increases exponentially.
2. For exponential growth, the base $b$ must satisfy $b > 1$.

Assessing the options:

We check which of the provided values satisfy $b > 1$:

• $0.35$: Not valid ($b < 1$).
• $1.3$: Valid ($b > 1$).
• $0.15$: Not valid ($b < 1$).
• $1.7$: Valid ($b > 1$).
• $1.8$: Valid ($b > 1$).
• $0.89$: Not valid ($b < 1$).
• $0.11$: Not valid ($b < 1$).
• $1.5$: Valid ($b > 1$).

Final Answer:

The possible values for $b$ are: $\boxed{1.3, 1.7, 1.8, 1.5}.$

Would you like further clarification or additional explanations?

Related Questions:

1. How does the value of $b$ affect the rate of exponential growth or decay?
2. What happens to the graph when $0 < b < 1$?
3. How can the initial value $a$ change the graph of an exponential function?
4. Can $b = 1$ ever represent exponential growth or decay? Why or why not?
5. What are the differences between exponential growth and linear growth in terms of their equations and graphs?

Tip:

To determine exponential growth or decay, always check whether $b > 1$ (growth) or $0 < b < 1$ (decay).