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To solve the question in the uploaded image, we need to calculate the **average rate of change** of the function \( f(t) = 1.6(1.3)^t \) between March 4 and March 26, 2020.

### Steps to Solve:

1. **Convert Dates to \( t \)-values**:
   - The function starts at \( t = 0 \) on February 29, 2020.
   - March 4 is 4 days after February 29, so \( t = 4 \).
   - March 26 is 26 days after February 29, so \( t = 26 \).

2. **Find \( f(4) \) and \( f(26) \)**:
   Substitute \( t = 4 \) and \( t = 26 \) into \( f(t) = 1.6(1.3)^t \):
   \[
   f(4) = 1.6(1.3)^4
   \]
   \[
   f(26) = 1.6(1.3)^{26}
   \]

3. **Calculate the Average Rate of Change**:
   The average rate of change formula is:
   \[
   \text{Average Rate of Change} = \frac{f(26) - f(4)}{26 - 4}
   \]

Let me compute the values. Function to compute the exponential growth
def f(t):
    return 1.6 * (1.3 ** t)

# Values for t
t_4 = 4
t_26 = 26

# Calculate f(4) and f(26)
f_4 = f(t_4)
f_26 = f(t_26)

# Calculate the average rate of change
average_rate_of_change = (f_26 - f_4) / (t_26 - t_4)
f_4, f_26, average_rate_of_changeHere are the results:

1. \( f(4) = 4.57 \) (approximately).
2. \( f(26) = 1467.73 \) (approximately).
3. The average rate of change from March 4 to March 26 is:
   \[
   \frac{f(26) - f(4)}{26 - 4} = \frac{1467.73 - 4.57}{22} \approx 66.51
   \]

### Correct Answer:
**a. 66.51**

Would you like more detailed steps or clarifications? Here are some related questions for further exploration:

1. What is the significance of the average rate of change in the context of exponential growth?
2. How does the growth factor (1.3) influence the results?
3. Can you find the instantaneous rate of change at a specific time \( t \)?
4. How would this function behave if the base of the exponent was reduced to 1.2?
5. What is the relationship between the average rate of change and the steepness of the curve?

**Tip:** Understanding exponential functions is crucial for modeling real-world scenarios such as population growth or epidemics!

A few weeks into the COVID-19 epidemic in 2020, the number of reported cases could be approximated by f(t) = 1.6(1.3)^t, where t is the number of days after February 29, 2020. What was the average rate of change of f(t) from March 4 to March 26?

Calculate the average rate of change for the exponential function f(t) = 1.6(1.3)^t modeling COVID-19 cases in March 2020. This problem highlights key concepts in exponential growth and algebra, suitable for Grades 10-12.

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