Question

Table
0 375,000
1 ?
2. ?
3 ?
4 ?
5 ?
The Diaz family purchased a home for $375,000 The decided to sell their home five years later. If the Caloocan the home is increasing at a rate of 6% each year, the situation can be modeled using the equation f(x)=375,000(1.06)^x. Finish the table to determine which graph displays the correct plotted points for the situation

Answer 1

To complete the table, we can use the function \( f(x) = 375,000(1.06)^x \) to calculate the value of the home after each year, for \( x = 0 \) to \( x = 5 \).

Here's how we can calculate each value step-by-step:

1. **For \( x = 0 \)**:
\[
f(0) = 375,000(1.06)^0 = 375,000 \text{ (This is already provided)}
\]

2. **For \( x = 1 \)**:
\[
f(1) = 375,000(1.06)^1 = 375,000 \times 1.06 = 397,500
\]

3. **For \( x = 2 \)**:
\[
f(2) = 375,000(1.06)^2 = 375,000 \times 1.1236 = 421,350
\]

4. **For \( x = 3 \)**:
\[
f(3) = 375,000(1.06)^3 = 375,000 \times 1.191016 = 446,127
\]

5. **For \( x = 4 \)**:
\[
f(4) = 375,000(1.06)^4 = 375,000 \times 1.26247696 = 472,194
\]

6. **For \( x = 5 \)**:
\[
f(5) = 375,000(1.06)^5 = 375,000 \times 1.338225 = 501,093.75 \approx 501,094 \text{ (rounding to the nearest whole number)}
\]

Now we can fill out the table:

| Year (x) | Home Value (f(x)) |
|----------|----------------------|
| 0 | 375,000 |
| 1 | 397,500 |
| 2 | 421,350 |
| 3 | 446,127 |
| 4 | 472,194 |
| 5 | 501,094 |

This completed table gives you the values for the home sale after each year. You can use these points to plot the graph accordingly.