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The problem you're working on involves exponential decay of a forest. Here’s how to approach each part:

### Part (a): Create an Exponential Function
The exponential function has the form:

\[
Q = Q_0 \times (1 + r)^t
\]

Where:
- \( Q_0 = 4000000 \) (the initial number of acres),
- \( r = -0.05 \) (since there is a 5% decay per year),
- \( t \) represents the time in years.

The equation becomes:

\[
Q = 4000000 \times (0.95)^t
\]

### Part (b): Create the Table for First 10 Years

For this, we calculate the quantity \( Q \) for each year by plugging the value of \( t \) into the function. Here's how you can calculate it:

1. **Year 0**: 
   \[
   Q = 4000000 \times (0.95)^0 = 4000000
   \]
2. **Year 1**:
   \[
   Q = 4000000 \times (0.95)^1 \approx 3800000
   \]
3. **Year 2**:
   \[
   Q = 4000000 \times (0.95)^2 \approx 3610000
   \]
4. **Year 3**:
   \[
   Q = 4000000 \times (0.95)^3 \approx 3430000
   \]
5. **Year 4**:
   \[
   Q = 4000000 \times (0.95)^4 \approx 3260000
   \]
6. **Year 5**:
   \[
   Q = 4000000 \times (0.95)^5 \approx 3100000
   \]

### Conclusion

- **Year 0**: 4,000,000 acres
- **Year 1**: 3,800,000 acres
- **Year 2**: 3,610,000 acres
- **Year 3**: 3,430,000 acres
- **Year 4**: 3,260,000 acres
- **Year 5**: 3,100,000 acres

Would you like further details on the calculations? Let me know if anything is unclear.

### Related Questions:
1. How do you compute the decay factor for different percentages?
2. What happens to the forest area after 10 years?
3. How does exponential decay differ from linear decay?
4. Can exponential growth models be used for population growth instead?
5. What would the equation look like if the growth rate were positive?

**Tip**: When dealing with exponential decay, always remember that the base of the exponent will be less than 1 (for decay).

A privately owned forest had 4,000,000 acres of old growth and is being cut down at a rate of 5% per year. Create an exponential function and a table for the first 10 years of decay.

Learn how to model the exponential decay of a 4,000,000-acre forest being cut down at 5% per year. This example includes the exponential function Q = 4000000 * (0.95)^t and a table showing forest area after each of the first 10 years.

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