Suppose that a two-bedroom house in Nashville is worth $\$110,000$ and appreciates at a rate of $2.5\%$ each year.

1. How much will it be worth in $10$ years?

   Hint (a):

   General form: $y=ab^x$

   Let $x =$ number of years and $y=$ value of house. Write an equation using the general form of the exponential equation.

   $a$ is the initial value of the house, and $b$ is the multiplier.

   Partial Answer (a):

   $y=110,000(1.025)^x$

2. When will it be worth $\$200,000$?

   Hint (b):

   Using the equation in part (a), guess and check values for $x$. Your answer will be approximate.

3. In Homewood, houses are depreciating at a rate of $5\%$ each year. If a house is worth $\$182,500$ now, how much will it be worth two years from now?

   Hint (c):

   Write another equation. Note that the value is depreciating this time.