Question

The median price of a home in Las Vegas, Nevada dropped from $312,346 in 2006 to $306,100 in 2007. Let t be the number of years since 2006.

Answer 1

Given:

Price in 2006 = $312,346

Price in 2007 = $306,100

Let's answer the following questions:

• (a). ,Let's write the linear equation representing this situation:

Apply the slope-intercept form:

y =mx + b

Where:

m is the slope and b is the initial value.

Let's find the slope using the slope formula:

$m=\frac{306100-312346}{2007-2006}=-6246$

Now, let's write the equation for P in terms of t.

$P\left(t\right)=-6246t+312346$

Where t is the number of years after 2006.

• The value of the home in 2 years.

Substitute 2 for t in the equation:

$\begin{gathered} P\left(2\right)=-6246(2)+312346 \\ \\ P(2)=-12492+312346 \\ \\ P(2)=299854 \end{gathered}$

The value of the home in 2 years is $299,854

• The value of the home in 3 years:

Substitute 3 for t and solve for P(3)

$\begin{gathered} P(3)=-6246\left(3\right)+312346 \\ \\ P(3)=293608 \end{gathered}$

The value of the house in 3 years is $293,608.

• (b). Let's write the equation exponentially.

We have:

$\begin{gathered} y=ab^x \\ \\ 306100=312346(b)^1 \\ \\ \frac{306100}{312346}=b^1 \\ \\ 0.98=b \end{gathered}$

Therefore, the exponential equation is:

$V(t)=312346(0.98)^t$

Value in 2 years:

$\begin{gathered} V(2)=312346(0.98)^2 \\ V(2)=299977.10 \end{gathered}$

Value in 3 years:

$\begin{gathered} V(3)=312346\left(0.98\right)^3 \\ V(3)=293977.56 \end{gathered}$

We have the graph below:

ANSWER:

Part A.

Equation: P(t) = -6246t + 312346

Value in 2 years, V(2) = $299,854

Value in 3 years, V(3) = $293,608

Part B.

Equation: V(t) = 312346(0.98)ˣ

V(2) = $299,977.10

V(3) = $293,977.56