### Home > A2C > Chapter 7 > Lesson 7.2.2 > Problem7-115

7-115.

The economy has worsened to the point that the merchants in downtown Hollywood cannot afford to replace their outdoor light bulbs when the bulbs burn out. On average, about thirteen percent of the light bulbs burn out every month. Assuming there are now about one million outside store lights in Hollywood, how long will it take until there are only $100,000$ bulbs lit? Until there is only one bulb lit?

Set up an exponential equation to represent this situation.

$y = 1,000,000\left(0.87\right)^{x}$

Let $y = 100,000$:

$100,000 = 1,000,000\left(0.87\right)^{x}$

To solve, divide both sides of the equation by $1,000,000$. Then take the log of both sides and apply the power property.