Question

the value of a house from the years 1955 - 2007 is given by the formula: $y = 3202x + 12400$ where $x$ is the number of years since 1955. what is the value of the house in 1967?
a) what would be the function notation for the value of the house in 1967
b) what is the value of the house in 1967?

Explanation:

Part b)

Step1: Calculate the number of years since 1955

To find \( x \) (the number of years since 1955) for the year 1967, we subtract 1955 from 1967. So, \( x = 1967 - 1955 = 12 \).

Step2: Substitute \( x \) into the formula

The formula for the value of the house is \( y = 3202x + 12400 \). Substitute \( x = 12 \) into this formula:
\[

$$\begin{align*} y&=3202\times12 + 12400\\ &= 38424 + 12400\\ &= 50824 \end{align*}$$

\]

Answer:

The value of the house in 1967 is 50824.