Noah and James want to sell their property. The property market is going down in their city and the expected properties’ value after 𝑚 months is given by the expression: 𝑃 equals the property value to start with multiplied by ninety five hundredths to the 𝑚 power. What is the percentage reduction in the property value per month?
Let’s think about this. What they’re saying is that we will need to multiply the value of the property by .95 to the power of whatever month they sell it in. And we are looking for the percentage reduction. Let me ask you a question. What would the formula be if the market was not going downhill? That is to say, what would the formula be if they could get out of their house exactly what they put into it, no matter how many months they waited. You would multiply the property value by one every time, no matter how many months you waited.
So let’s compare these two formulas. On the one hand, we have the formula if the market is not going down. And you multiply by one. On the other hand, we have .95. What is the reduction here? What is the percent reduction? If we take away the 95 hundredths from one, we’re left with five hundredths. And five hundredths in percentage form is five percent. The percent reduction for their home value is five percent.