SOLUTION: Hello, could someone please help me with a two part problem writing equations? The problem states: Houses in Madison's town are losing 11% of their value each year. Let v be the

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Hello, could someone please help me with a two part problem writing equations? The problem states: Houses in Madison's town are losing 11% of their value each year. Let v be the      Log On


   

Question 1026874: Hello, could someone please help me with a two part problem writing equations? The problem states: Houses in Madison's town are losing 11% of their value each year. Let v be the current value of Madison's house. Write an equation that describes the projected value, p, at a time, t, years from now. I have P=V(1-r)^t and after substituting 11 for r, I got the equation P=V(0.89)^t. Then, the next part states "Rewrite your equation to find the effective monthly percentage decrease in value". I thought it might be V=(1-0.11/12)^12t, but I'm not sure. Any help would be appreciated!
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
You want to change the equation from viewing as a yearly period to view as a monthly period.

1-11%2F12 will give the rate kept for a one-month period.

Next is to make the adjustment for amount of time. t is still YEARS. You know the fact 12 months IS 1 year.
t%2Ayears%2A12%28months%2Fyear%29=12t%2Amonths, so you seem to ALMOST have the formula correct -----just need the proper grouping symbols for the rendering into "notation".

P=V%281-r%2F12%29%5E%2812t%29-------------but remember --- t is used in YEARS.