Wilson is thinking about buying a house for $249,000. the table below shows the projected value of two different houses for three years. number of years 1 2 3 house 1 (value in dollars) 253,980 259,059.60 264,240.79 house 2 (value in dollars) 256,000 263,000 270,000 part a: what type of function, linear or exponential, can be used to describe the value of each of the houses after a fixed number of years? explain your answer. (2 points) part b: write one function for each house to describe the value of the house f(x), in dollars, after x years. (4 points) part c: wilson wants to purchase a house that would have the greatest value in 45 years. will there be any significant difference in the value of either house after 45 years? explain your answer, and show the value of each house after 45 years. (4 points)

From the table it can be seen that house 2 increases by the same value each year. i.e. house 2 increases by $7,000 every year. (263,000 - 256,000 = 7,000 and 270,000 - 263,000 = 7,000)it can also be seen that house 1, increases at a constant percent with respect to the previous year. i.e. house 1 increases at the rate of 2% every year.thus, the value of house 1 after a fixed number of years can be described by an exponential function while the the value of house 2 after a fixed number of years can be described by a linear function.part b: given that house 1 increases at a constant rate of 2% every year with the initial price at $249,000. the function that describes the value of the house f(x), in dollars, after x years is given bygiven that house 2 increases by $7,000 every year with the initial price at $249,000. the function that describes the value of the house f(x), in dollars, after x years is given bypart c: given that the function that describes the value of the house 1 f(x), in dollars, after x years is given byafter 45 years, the value of the house will begiven that the function that describes the value of the house 2 f(x), in dollars, after x years is given byafter 45 years, the value of the house will betherefore, house 1 will have the greater value after 45 years.

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