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Jillian's parents bought a house for $450,000, and the value of the house has been increasing steadily by 3% each year.

a. Find the formula that represents the value of the house each year.

b. If Jillian's parents sell their house 10 years after they bought it, how much profit will they make? (That is, how much more are they selling it for than they bought it for?) Express your answer as both a dollar amount and a percent of the original purchase price.

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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%

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