Find C and a so that f(x) = Ca^x models the situation described. State what the variable X represents in your formula.

Question

Find C and a so that f(x) = Ca^x models the situation described. State what the variable X represents in your formula.

 

In 2000 a house was worth $220,000 and its value decreases by 11% each year thereafter.

 

 

C = ?

Answer 1

f( X) = C a^x

 

      C represent the value of house in year 2000 which was 220,000.

 

   a should be ( 1 - 0.11) = 0.89

 

      x - number of years after year 2000.

        

      each year reduces by 89 % .

Answer 2

f(x) = Ca^x

 

x = years since 2000.

 

f(0) = 220000 = Ca^0 = C

 

f(x) = 220000a^x

 

f(1) = 220000(1-0.11) = 220000a^1

 

a = 0.89

 

f(x) = 220000(0.89)^x