Your grandfather purchased a house for $45,000 in 1952 and it has increased in value according to a function y = v(x), where x is the number of years owned. These questions probe the future value of the house under various mathematical models. (Let x = 0 represent the year 1952.)(a) Suppose the value of the house is $60,000 in 1962. Assume v(x) is a linear function. Find a formula for v(x). v(x) = .
What is the value of the house in 1995? $ .
Using this model, in what year will the house be valued at $200,000? (Round your answer to the nearest year.)
(b) Suppose the value of the house is $60,000 in 1962 and $130,000 in 1967. Assume v(x) is a quadratic function. Find a formula for v(x). (Round your values to two decimal places.) v(x) = .
What is the value of the house in 1995? $ .
Using this model, in what year will the house be valued at $200,000? (Round your answer to the nearest year.)