Question

life expectancy in exercises 14 and 15, use the information in the table, which gives the life expectancy in the united states for a child (at birth).

year	1930	1940	1950	1960	1970	1980	1990	2000
life expectancy (years)	59.7	62.9	68.2	69.7	70.8	73.7	75.4	76.4

1. in which decade did life expectancy increase the most?
2. construct a line graph of these data and discuss what the line graph shows.

Explanation:

Step1: Calculate life - expectancy increase per decade

1930 - 1940: $62.9−59.7 = 3.2$
1940 - 1950: $68.2−62.9 = 5.3$
1950 - 1960: $69.7−68.2 = 1.5$
1960 - 1970: $70.8−69.7 = 1.1$
1970 - 1980: $73.7−70.8 = 2.9$
1980 - 1990: $75.4−73.7 = 1.7$
1990 - 2000: $76.4−75.4 = 1$

Step2: Compare the increases

We compare the values $3.2,5.3,1.5,1.1,2.9,1.7,1$. The largest value is $5.3$.

Answer:

The 1940 - 1950 decade.

For constructing a line graph:

• On the x - axis, we mark the years 1930, 1940, 1950, 1960, 1970, 1980, 1990, 2000.
• On the y - axis, we mark the life - expectancy values starting from a value slightly below 59.7 (e.g., 59) and going up to a value slightly above 76.4 (e.g., 77).
• We plot the points $(1930,59.7),(1940,62.9),(1950,68.2),(1960,69.7),(1970,70.8),(1980,73.7),(1990,75.4),(2000,76.4)$ and connect them with line segments.

The line graph shows a general upward trend in life - expectancy over the years from 1930 to 2000 in the United States, with some decades having larger increases than others. The steepest increase is seen in the 1940 - 1950 decade, which is consistent with our previous calculation.