In Country X, the average hourly wage in dollars from 1960 to 2010 can be modeled by $$f ( x ) = \left\{ \begin{array} { l l }
0.075 ( x - 1960 ) + 0.39 & \text { if } 1960 \leq x

Question

In Country X, the average hourly wage in dollars from 1960 to 2010 can be modeled by $$f ( x ) = \left\{ \begin{array} { l l } 
0.075 ( x - 1960 ) + 0.39 & \text { if } 1960 \leq x < 1985 \
0.181 ( x - 1985 ) + 3.05 & \text { if } 1985 \leq x \leq 2010
\end{array} \right.$$ Use f to estimate the average hourly wages in 1965, 1985, and 2005.
A) $0.77, $2.27, $6.67
B) $3.43, $0.39, $6.67
C) $0.77, $3.05, $6.67

Quizplus · Accepted Answer

For 1965, use the first equation with $x = 1965$: $0.075(1965 - 1960) + 0.39 = 0.75 + 0.39 = 0.77$. For 1985, the first equation directly gives the transition value: $0.075(1985 - 1960) + 0.39 = 3.05$. For 2005, use the second equation with $x = 2005$: $0.181(2005 - 1985) + 3.05 = 3.62 + 3.05 = 6.67$.

In Country X, the Average Hourly Wage in Dollars from 1960