Your grandfather purchased a house for $55,000 in 1952 and it has increased in v

Question

Your grandfather purchased a house for $55,000 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.)

b) Suppose the value of the house is $75,000 in 1962 and $160,000 in 1967. Assume v(x) is a quadratic function. Find a formula for 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?

(c) Suppose the value of the house is $75,000 in 1962. Assume v(x) is a function of exponential type. Find a formula for 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?

Explanation / Answer

(c)

Exponential function is of the form:

v(x) = v? a?
where v? = initial value = 55,000

v(x) = 55000 a?

Now we know that in 1962 (x = 10), value of the house is $75,000
v(10) = 75000
55000 a¹? = 75000
a¹? = 75000/55000
a¹? = 15/11
a = (15/11)^(1/10)
a = 1.03150148464

Rounding a to 4 decimal places, we get:

v(x) = 55000 (1.0315)?

In 1995, x = 43 =======> v(43) = 55000*(1.0315)^43 = 208708.3

Now

200000 = 55000 (1.0315)?

x = 41.6 ======> Means in 1952 + 41 = 1991

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.