To determine the values of $b$ and $k$ for the function $f(x) = 5(b)^x + k$, we need to analyze the given information and the graph.

Key Observations:

1. Horizontal Asymptote: $y = 1$ implies $k = 1$ because as $x \to \infty$, the value of $f(x)$ approaches $k$.

   • Thus, $k = 1$.

2. Exponential Decay: The problem states a constant percent rate of change of 80%. This means that the function retains 80% of its previous value as $x$ increases by 1.

   • The decay factor $b$ is equal to $0.8$.

Final Values:

• $b = 0.8$
• $k = 1$

Would you like a deeper explanation or verification using points from the graph? Here are some related questions to expand on the topic:

1. How is the horizontal asymptote related to the value of $k$?
2. How can you calculate the decay factor from the graph?
3. What does the constant percent rate of change signify in an exponential function?
4. How does the $y$-intercept affect the function's formula?
5. How can you verify the solution using specific points from the graph?

Tip: To verify your results, substitute a known point from the graph (like $(0, 6)$) into the equation and confirm it holds true!