Question

Y=7.40*(1.619)^× round to nearest hundred exponential model

Answer 1

To round the expression \( Y = 7.40 \times (1.619)^x \) to the nearest hundred for values of \( Y \), you need to calculate \( Y \) for specific values of \( x \) and then round the result.

Here's how to do it step by step:

1. **Choose a value for \( x \)**.
2. **Calculate \( Y \)** using the formula.
3. **Round \( Y \)** to the nearest hundred.

Let's illustrate this by calculating \( Y \) for some sample values of \( x \):

### Example Calculations

1. **For \( x = 0 \)**:
\[
Y = 7.40 \times (1.619)^0 = 7.40 \times 1 = 7.40
\]
Rounding 7.40 to the nearest hundred gives **0**.

2. **For \( x = 1 \)**:
\[
Y = 7.40 \times (1.619)^1 = 7.40 \times 1.619 \approx 11.99
\]
Rounding 11.99 to the nearest hundred gives **0**.

3. **For \( x = 2 \)**:
\[
Y = 7.40 \times (1.619)^2 \approx 7.40 \times 2.621 \approx 19.42
\]
Rounding 19.42 to the nearest hundred gives **0**.

4. **For \( x = 3 \)**:
\[
Y = 7.40 \times (1.619)^3 \approx 7.40 \times 4.249 \approx 31.42
\]
Rounding 31.42 to the nearest hundred gives **0**.

5. **For \( x = 10 \)**:
\[
Y = 7.40 \times (1.619)^{10} \approx 7.40 \times 48.29 \approx 357.43
\]
Rounding 357.43 to the nearest hundred gives **400**.

6. **For \( x = 20 \)**:
\[
Y = 7.40 \times (1.619)^{20} \approx 7.40 \times 2322.89 \approx 17200.95
\]
Rounding 17200.95 to the nearest hundred gives **17200**.

### Conclusion
You can apply this method to obtain \( Y \) for any \( x \) value, and simply round the result to the nearest hundred accordingly. If you have a specific value of \( x \) in mind that you want to calculate and round, please provide it!