A certain car depreciates such that its value at the end of each year is p % less than its value at the end of the previous year. If that car was worth a dollars on December 31, 2010 and was worth b dollars on December 31, 2011, what was the car worth on December 31, 2013 in terms of a and b ?

Answer:b(b/a)^2Step-by-step explanation:Given that the value of the car depreciates such that its value at the end of each year is p % less than its value at the end of the previous year and that car was worth a dollars on December 31, 2010 and was worth b dollars on December 31, 2011, thenb = a - (p% × a) = a(1-p%)b/a = 1 - p%p% = 1 - b/a = (a-b)/aLet the worth of the car on December 31, 2012 be cthen c = b - (b × p%) = b(1-p%)Let the worth of the car on December 31, 2013 be dthen d = c - (c × p%)d = c(1-p%)d = b(1-p%)(1-p%)d = b(1-p%)^2d = b(1- (a-b)/a)^2d = b((a-a+b)/a)^2d = b(b/a)^2 = b^3/a^2The car's worth on December 31, 2013 =  b(b/a)^2 = b^3/a^2