The value of a family's home, in Camrose AB, is given by the following exponential function f(x), where x is the number of years
after the family purchases the house for $130,000. What is the best estimate for the instantaneous rate of change in the value of the home when the family has owned it for 5 years? f(x) =130000(1.06)^x
Given the value of a family's home, in Camrose AB, given by the following exponential function f(x) = 130000(1.06)^x, where x is the number of years after the family purchases the house for $130,000. In order to calculate the best estimate for the instantaneous rate of change in the value of the home when the family has owned it for 5 years, we will have to substitute x =5 in the given function and solve as shown;
f(x) = 130000(1.06)ˣ
f(5) = 130000(1.06)⁵
f(5) = 130000*(1.06)⁵
f(5) = 130000*1.338226
f(5) = 173,969.38
Hence, the instantaneous rate of change in the value of the home when the family has owned it for 5 years is approximately $173,969
