Let's analyze the exponential function given in the problem:

The function is: $f(x) = 320 \cdot (0.90)^x$

This function indicates an exponential decay model, where the base $0.90$ is less than 1, showing that the price decreases over time.

1. Initial Price: The initial price before any adjustments (when $x = 0$) is found by substituting $x = 0$ into the function: $f(0) = 320 \cdot (0.90)^0 = 320$ So, the initial price is $320 (Answer: B for question 2).

2. Price Change: Since the base of the exponent $0.90$ is less than 1, the price is decreasing (Answer: B for question 3).

3. Rate of Change: The rate of change each week is $10\%$ since $0.90$ represents a decrease of $10\%$ each week (Answer: A for question 4).

Final Answers:

• Question 2: $320
• Question 3: decreases
• Question 4: 10%

Would you like further details on any of these answers?

Here are some related questions for deeper understanding:

1. How would the function change if the price increased each week?
2. What would be the price after 5 weeks with this model?
3. How would a 20% weekly decrease affect the initial model?
4. If the initial price was different, how would it affect the function?
5. What is the impact of exponential decay in real-world pricing?

Tip: In exponential decay, a base between 0 and 1 indicates a decrease, while a base greater than 1 indicates an increase.