Problema Solution
A family purchased a condo for $80,000. Each year the value of the condo increases by 5%. Write a function that models the value of the house over time. Then find the value of the house after 6 years. Round your answer to the nearest dollar.
Answer provided by our tutors
let f(x) be the function that models the value of the house over time and x = the number of of year
when they bought the house: x = 0
f(0) = 80,000
after 1 year: x = 1
f(1) = f(0) + 0.05*f(0) = f(0)(1 + 0.05) = 1.05*f(0)
after 2 years: x = 2
f(2) = 1.05*f(1) = (1.05)^2 * f(0)
after n years: x = n
f(n) = (1.05)^n * f(0)
lets find the value after 6 years: x = 6
f(6) = (1.05)^6 * f(0)
f(6) = (1.05)^6 * 80000
f(6) = $107,208