Question

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

Answer 1

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