Question

1. if the value of a house in 2005 was $100,000 and was valued at $140,000 in 2010, what was the value in 1999, assuming the appreciation was linear? 13. the...

Explanation:

Step1: Define linear appreciation model

Let $t$ = years since 1999, $V(t)$ = house value. Model: $V(t)=mt+b$, where $b$ is 1999 value.

Step2: Assign t values to given years

2005: $t=2005-1999=6$, $V(6)=100000$; 2010: $t=2010-1999=11$, $V(11)=140000$

Step3: Calculate slope m

Slope formula: $m=\frac{V(11)-V(6)}{11-6}$
$m=\frac{140000-100000}{5}=\frac{40000}{5}=8000$

Step4: Solve for b (1999 value)

Substitute $m=8000$, $t=6$, $V(6)=100000$ into $V(t)=mt+b$:
$100000=8000\times6 + b$
$100000=48000 + b$
$b=100000-48000=52000$

Answer:

$\$52,000$