houses in Madisons town are losing 11 of their value each ye

3. Houses in Madison\'s town are losing 11% of their value each year. a) 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. b) Rewrite your equation to find the effective monthly percentage decrease in value. p-

Solution

Let :

v = current value of Maddys house

p = projected value

t = time

current value minus the 11% lost of value per year = the projected value

r = 11% = 0.11

So, p = v ( 1 - r)^t

p = v ( 1 - 0.11 )^t

Hence p = v ( 0.89)^t annual decline in house prices.

#(b)

since we are calculating monthly now

Hence, p = v * 0.990336^(12t)