5. Linda bought a house in 2006 for $150,000 and, in 2011, it was assessed (valu

Question

5. Linda bought a house in 2006 for $150,000 and, in 2011, it was assessed (valued) at $153,000. Assume also bought a house in 2006 the value of Linda's house grows according to a linear whose assessed value changes according to B(t)958+16083+ 120000. (4 pts each) (a) Find a formula in the form L( mt t b for the value L) of Linda's house t years after model. Bert ram 2006. (b) Linda wants to sell her house in 2019. What will the house be worth acording to this model? (c) What is the maximum assessed value of Bertram's house? (d) In what year(s) will the value of Bertram's house be the same as Linda's?

Explanation / Answer

5. Points are (0,150000),(5,153000)

Slope , m = (153000-150000)/(5-0) = 3000/5=600

a. L(t) = 600t + 150000

b. 2019 means t= 2019-2006=13

L(13)= 600(13)+150000 = $157800

c.B(t)=-958t2+16083t+120000

t= -16083/2(-958) =8.394

B(8.394) =-958(8.314)2+16083(8.394) +120000=$188781

d.600t +150000=-958t2+16083t+120000

958t2-15483t +30000=0

t=2.25, 13.91years

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