Final answer:
The value of the house each year can be calculated with the exponential growth formula V = $450,000(1 + 0.03)^t.
If Jillian's parents sell the house after 10 years, they would make a profit of approximately $153,568.77, which is about 34.13% of the original purchase price.
Step-by-step explanation:
To find the formula that represents the value of Jillian's parents' house each year, we need to use the formula for exponential growth.
The general formula is P(1 + r)^t, where P is the original amount, r is the rate of increase, and t is the time in years.
For this scenario:
- P = $450,000 (the original value of the house)
- r = 0.03 (3% increase per year)
- t = the number of years since the house was bought
So the formula representing the value V of the house each year is:
V = $450,000(1 + 0.03)^t.
Now, to calculate the profit Jillian's parents would make if they sell the house 10 years after they bought it, we substitute t with 10:
V = $450,000(1 + 0.03)^{10}
After calculating, the value of the house after 10 years (V) would be approximately $603,568.77.
To find the profit, we subtract the original purchase price from this amount:
Profit = V - Original Purchase Price
Profit = $603,568.77 - $450,000
= $153,568.77
To express this profit as a percent of the original purchase price:
Percent Profit = (Profit / Original Purchase Price) * 100%
Percent Profit = ($153,568.77 / $450,000) * 100%
≈ 34.13%