The following table shows the approximate average household income in the U.S. in 1990, 2002, and 2003. ( $t = 0$ represents 1990.) $$\begin{array} { | r | c | c | c | }
\hline \boldsymbol { t } \text { (Year) } & 0 & 12 & 13 \
\hline \boldsymbol { H } \text { (Household Income in \$1000) } & 30 & 42 & 43 \
\hline
\end{array}$$ Which of the following kinds of models would best fit the given data (A, a, b, c, and m are constants.)

A)Exponential: $V ( t ) = A ^ { b \cdot t }$
B) Logarithmic: $V ( t ) = A \cdot \ln ( b \cdot t )$
C) Linear: $V ( t ) = m \cdot t + b$
D) Quadratic: $V ( t ) = a \cdot t ^ { 2 } + b \cdot t + c$
E) Power: $V ( t ) = a \cdot ( t + b ) ^ { 4 } + c$

Question

The following table shows the approximate average household income in the U.S. in 1990, 2002, and 2003. ( $t = 0$ represents 1990.) $$\begin{array} { | r | c | c | c | } 
\hline \boldsymbol { t } \text { (Year) } & 0 & 12 & 13 \
\hline \boldsymbol { H } \text { (Household Income in \$1000) } & 30 & 42 & 43 \
\hline
\end{array}$$  Which of the following kinds of models would best fit the given data  (A, a, b, c, and m are constants.)

A)Exponential: $V ( t ) = A ^ { b \cdot t }$
B) Logarithmic: $V ( t ) = A \cdot \ln ( b \cdot t )$
C) Linear: $V ( t ) = m \cdot t + b$
D) Quadratic: $V ( t ) = a \cdot t ^ { 2 } + b \cdot t + c$
E) Power: $V ( t ) = a \cdot ( t + b ) ^ { 4 } + c$

Quizplus · Accepted Answer

The data shows a consistent increase in household income over time, which suggests a linear relationship between time and income. This is best represented by the linear model $V(t) = m \cdot t + b$, where $m$ is the slope (rate of change) and $b$ is the y-intercept (starting value).

The Following Table Shows the Approximate Average Household Income in the U.S