To match each equation to the appropriate graph, let’s analyze the equations and the general shapes of the graphs:

1. Equation Analysis:

   • $y = 1,000(0.95)^x$: This is an exponential decay function, since the base of the exponent (0.95) is less than 1. We expect a graph that starts high and decreases over time.
   • $y = 200 + 11x$: This is a linear function with a positive slope, indicating a straight line that increases as $x$ increases.
   • $y = 5(1.1)^x$: This is an exponential growth function, since the base (1.1) is greater than 1. We expect a graph that starts low and increases sharply as $x$ increases.

2. Graph Analysis:

   • Graph A shows an exponential growth shape: it starts low and increases rapidly. This graph matches the exponential growth function $y = 5(1.1)^x$.
   • Graph B shows an exponential decay shape: it starts high and decreases over time. This graph matches the exponential decay function $y = 1,000(0.95)^x$.
   • Graph C is a straight line with a positive slope, which corresponds to a linear equation. This graph matches $y = 200 + 11x$.

3. Matching Each Graph to an Equation:

   • Graph A: $y = 5(1.1)^x$
   • Graph B: $y = 1,000(0.95)^x$
   • Graph C: $y = 200 + 11x$

Would you like more details on exponential functions or how to interpret these graphs?

Here are five questions to expand on this topic:

1. What are the general characteristics of exponential decay and growth functions?
2. How can we determine if a function is linear or non-linear by looking at its equation?
3. How does changing the base in an exponential function affect the graph's shape?
4. What are some real-world examples of exponential growth and decay?
5. How can you tell the difference between exponential and linear functions just by observing a graph?

Tip: Exponential growth and decay functions are often used to model populations and radioactive decay, respectively. Recognizing their graphs can help you understand these phenomena better!