Problema Solution
Six years ago a house was purchased for $179,000. This year it was appraised at $215,000. Assume that the value V of the house after its purchase is a liner function of time t (in years).
(A) Express V in terms of t.
(B) How many years after the purchase date was the house worth $193,000.
Answer provided by our tutors
(A)
V(t) = at + b, where a and b are constants
V(0) = 179,000
v(6) = 215,000
We have the following system of equations:
a*0 + b = 179,000
6a + b = 215,000
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click here to see the system of equations solved for a and b
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a = 6,000
b = 179,000
The expression for V is:
V(t) = 6,000t + 179,000
(B)
Let t represent the time in years.
We need to find t such that V(t) = 193,000
6,000t + 179,000 = 193,000 divide both sides by 1,000
6t + 179 = 193
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click here to solve the equation for t
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t = 7/3 years
t = 2 years 1*12/3 months
t = 2 years 4 months
After 2 years and 4 months the house will be worth $193,000.