Question

math 112 midterm 2 practice exam 2 page 4 the following graph shows the average height of men by year for france and for the usa. call these functions ( h_{f}(y) ) and ( h_{s}(y) ), where ( y ) is measured in years since 1810. use these graphs to answer the next two questions. average height of men by year of birth 9. estimate ( h_{f}(90) ) and give a practical interpretation. (a) ( h_{f}(90)=166 ). the average height of french men 90 years after 1810 was 166 cm. (b) ( h_{f}(90)=167 ). the average height of french men 90 years after 1810 was 167 cm. (c) ( h_{f}(90)=169 ). the average height of french men 90 years after 1810 was 169 cm. (d) ( h_{f}(90)=170 ). the average height of french men 90 years after 1810 was 170 cm. (e) ( h_{f}(90)=176.5 ). the average height of french men 90 years after 1810 was 176.5 cm. 10. estimate ( left(h_{s}-h_{f}
ight)(90) ) and give a practical interpretation. (a) ( left(h_{s}-h_{f}
ight)(90) ) cannot be determined. (b) ( left(h_{s}-h_{f}
ight)(90)=-2 ). ninety years after 1810, the average height of american men is 2 cm less than the average height of french men. (c) ( left(h_{s}-h_{f}
ight)(90)=2 ). ninety years after 1810, the average height of american men is 2 cm more than the average height of french men. (d) ( left(h_{s}-h_{f}
ight)(90)=-3 ). ninety years after 1810, the average height of american men is 3 cm less than the average height of french men. (e) ( left(h_{s}-h_{f}
ight)(90)=3 ). ninety years after 1810, the average height of american men is 3 cm more than the average height of french men.

Explanation:

Step1: Analyze the graph for \(h_{f}(90)\)

Locate \(y = 90\) on the x - axis (years since 1810). Then, find the corresponding value on the \(h_{f}(y)\) (French men's height) curve. By visual inspection of the graph, when \(y=90\), \(h_{f}(90)\approx166\)

Step2: Analyze the graph for \((h_{a}-h_{f})(90)\)

First, find \(h_{a}(90)\) (American men's height at \(y = 90\)) and \(h_{f}(90)\). Then calculate \(h_{a}(90)-h_{f}(90)\). From the graph, \(h_{a}(90)\approx168\) and \(h_{f}(90)\approx166\), so \((h_{a}-h_{f})(90)=168 - 166=2\)

Answer:

1. A. \(h_{f}(90)=166\). The average height of French men 90 years after 1810 was 166 cm.
2. C. \((h_{a}-h_{f})(90)=2\). Ninety years after 1810, the average height of American men is 2 cm more than the average height of French men.