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45. Real Estate Appreciation Bob Michaels purchased a
house 8 years ago for $42,000. This year it was appraised at
$67,500.
(a) A linear equation V = mt + b, 0 the value V of the house for 15 years after it was pur-
chased. Determine m and b.
(b) Graph the equation and trace to estimate in how many years
after purchase this house will be worth $72,500.
(c) Write and solve an equation algebraically to determine
how many years after purchase this house will be worth
$74,000.
(d) Determine how many years after purchase this house will
be worth $80,250.
19

Respuesta :

mhanifa

Answer:

a)

Since t is between 0 and 15, and the house was purchased 8 years ago, we have two pairs of values:

  • t = 0, V(0) = 42000
  • t = 8, V(8) = 67500

Find the slope, m:

  • m = (67500 - 42000)/8 = 3187.50

The value of b is 42000, since at t = 0, V = 42000

So the equation is:

  • V = 3187.50t + 42000

b)

The graph is attached.

When V = 72500, t = 9.6 (approximately)

c)

When V = 74000

  • 74000 = 3187.5t + 42000
  • 3187.5t = 32000
  • t = 32000/3187.5
  • t ≈ 10 years (rounded down)

d)

When V = 80250

  • 80250 = 3187.5t + 42000
  • 3187.5t = 80250 - 42000
  • 3187.5t = 38250
  • t = 38250/3187.5
  • t = 12 years
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