### Home > AC > Chapter 13 > Lesson 13.OF2-S > Problem7-147

7-147.

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?

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.

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

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

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?

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