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To solve the problem, we need to find the exponential model of the form \( A(t) = Pe^{rt} \). Given the initial conditions:

- Initially (\( t = 0 \)), there are 48 confirmed cases.
- 6 days later (\( t = 6 \)), there are 70 confirmed cases.

1. **Determine \( P \):**
   
   The initial number of infected cases is \( P \), which is given directly:
   \[
   P = 48
   \]

2. **Determine \( r \):**

   Use the information for \( t = 6 \) and \( A(6) = 70 \):
   \[
   70 = 48e^{6r}
   \]
   Solving for \( r \):
   \[
   \frac{70}{48} = e^{6r}
   \]
   \[
   \ln\left(\frac{70}{48}\right) = 6r
   \]
   \[
   r = \frac{\ln\left(\frac{70}{48}\right)}{6}
   \]

   Calculate \( r \):
   \[
   r = \frac{\ln\left(\frac{70}{48}\right)}{6} \approx \frac{\ln(1.4583)}{6} \approx \frac{0.3771}{6} \approx 0.06285
   \]

   Rounded to thousandths:
   \[
   r \approx 0.063
   \]

3. **Growth rate as a percent:**

   The growth rate as a percent is:
   \[
   r \times 100 \approx 0.063 \times 100 \approx 6.3\%
   \]

Thus, the answers are:

- \( P = 48 \)
- \( r \approx 0.063 \)
- Growth rate: 6.3%

Do you have any questions or need further details?

Here are 5 questions you might have:
1. How do you calculate the natural logarithm?
2. Can you explain how to solve exponential equations in more detail?
3. How would the model change if the growth rate were different?
4. Can this method be used for other types of growth, like population growth?
5. What are some common applications of exponential growth models?

Tip: Understanding the process of solving for \( r \) involves knowing how to manipulate exponential and logarithmic equations, which is crucial in many fields including biology, finance, and physics.

Learn how to solve an exponential growth model problem where initial confirmed cases and growth rate are determined. Step-by-step solution includes calculating initial cases, finding growth rate, and interpreting results. Suitable for high school students studying exponential functions.

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