Question

A house currently valued at $250,000 increases in value at the rate of 4% per year.

Which exponential equation models this situation?

(1 point)
Responses

y=250,000+1.04xy is equal to 250 comma 000 plus 1 point 0 4 x

y=250,000(1.04)xy is equal to 250 comma 000 times 1 point 0 4 to the x th power

y=250,000(0.04)xy is equal to 250 comma 000 times 0 point 0 4 to the x th power

y=250,000x1.04y is equal to 250 comma 000 x raised to the 1 point 0 4 power
Question 2
A house currently valued at $250,000 increases in value at the rate of 4% per year.(1 point)
What will the value of the house be in 15 years? Round to the nearest dollar (one's place).

Answer 1

For Question 1, the correct exponential equation that models the situation is:

**\( y = 250,000(1.04)^x \)**

This equation represents the current value of the house growing at a rate of 4% per year, where \( x \) is the number of years.

---

For Question 2, to find the value of the house in 15 years using the equation \( y = 250,000(1.04)^x \):

1. Plug in \( x = 15 \):
\[
y = 250,000(1.04)^{15}
\]

2. Calculate \( (1.04)^{15} \):
\[
(1.04)^{15} \approx 1.747422
\]

3. Now calculate \( y \):
\[
y \approx 250,000 \times 1.747422 \approx 436,855.50
\]

4. Round to the nearest dollar:
\[
y \approx 436,856
\]

Therefore, the value of the house in 15 years will be approximately **$436,856**.