A study found that the divorce rate d (given as a percentage) appears to depend on the ratio r of available men to available women. This function can be approximated by $$d ( r ) = \left\{ \begin{array} { l l }
- 40 r + 100 & \text { if } r \leq 1.3 \
\frac { 101 r } { 4 } - \frac { 118 } { 4 } & \text { if } r 1.3
\end{array} \right.$$
There are currently 0.8 available men per available woman in Littleville, and this ratio is increasing by 0.1 per year. At what percent is the divorce rate decreasing

A)0.4% per year
B) 0.08% per year
C) 10% per year
D) 4% per year
E) 10.1% per year

Question

A study found that the divorce rate d (given as a percentage) appears to depend on the ratio r of available men to available women. This function can be approximated by   $$d ( r ) = \left\{ \begin{array} { l l } 
- 40 r + 100 & \text { if } r \leq 1.3 \
\frac { 101 r } { 4 } - \frac { 118 } { 4 } & \text { if } r > 1.3
\end{array} \right.$$  
There are currently 0.8 available men per available woman in Littleville, and this ratio is increasing by 0.1 per year. At what percent is the divorce rate decreasing 
 
A)0.4% per year
B) 0.08% per year
C) 10% per year
D) 4% per year
E) 10.1% per year

Quizplus · Accepted Answer

The divorce rate is decreasing by 4% per year because the ratio of available men to available women is increasing by 0.1 per year, and the divorce rate is a decreasing function of this ratio.

A Study Found That the Divorce Rate D (Given as a Percentage)