st-math1-q27

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The figure shows a horizontal bar graph. The graph is titled '2000 Population.' The horizontal axis is labeled 'Population in millions.' The integers 0 to 50, in increments of 10, are indicated on the horizontal axis. The vertical axis is labeled 'Age Group in years,' and there are 9 age groups indicated along the vertical axis. The age groups are 0 to 9, 10 to 19, 20 to 29, 30 to 39, 40 to 49, 50 to 59, 60 to 69, 70 to 79, and the ninth age group is 80 plus. For each age group, there is a horizontal bar associated with it. The length of the bar represents population. The 2000 population for the 9 age groups are as follows. Age group 0 to 9, 39 million. Age group 10 to 19, 40 million.

The figure shows a horizontal bar graph. The graph is titled '2050 Projected Population.' The horizontal axis is labeled 'Population in millions.' The integers 0 to 60, in increments of 10, are indicated on the horizontal axis. The vertical axis is labeled 'Age Group in years,' and there are 9 age groups indicated along the vertical axis. The age groups are 0 to 9, 10 to 19, 20 to 29, 30 to 39, 40 to 49, 50 to 59, 60 to 69, 70 to 79, and the ninth age group is 80 plus. For each age group, there is a horizontal bar associated with it. The length of the bar represents population.

The graphs above show United States Census Bureau population figures for the year $2000$ for various age groups, together with projections for the year $2050$ . Of the following age groups, for which is the projected percent increase in population from $2000$ to $2050$ greatest?

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$30 minus 39$

Correct Answer:

$40 minus 49$

Correct Answer:

$50 minus 59$

Correct Answer:

$60 minus 69$

Correct Answer:

Yes

$70 minus 79$

Correct Answer:

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The correct answer is D.

To determine for which of the five age groups in the options the projected percent increase in population from $2000$ to $2050$ is greatest, estimate the ratio of the projection for the year $2050$ to the population figure for $2000$ for each age group. Each of the ratios described is equal to $1$ plus the decimal corresponding to the projected percent increase in population from $2000$ to $2050$ , so the greatest ratio will correspond to the greatest projected percent increase in population.

For the $30 - 39$ age group, the ratio is less than $\frac{60}{40} = 1.5$ , since the $2050$ projected population is less than $60$ million and the $2000$ population is greater than $40$ million. Thus the projected percent increase in population from $2000$ to $2050$ for this age group is less than $50$ percent.

For the $40 - 49$ age group, the ratio is less than $\frac{50}{40} = 1.25$ , since the $2050$ projected population is less than $50$ million and the $2000$ population is greater than $40$ million. Thus the projected percent increase in population from $2000$ to $2050$ for this age group is less than $25$ percent.

For the $50 - 59$ age group, the ratio is less than $\frac{50}{30} = 1.6 \bar{6}$ , since the $2050$ projected population is less than $50$ million and the $2000$ population is greater than $30$ million. The projected percent increase in population from $2000$ to $2050$ for this age group is less than $66$ percent.

For the $60 - 69$ year age group, the ratio is approximately $41$ million to $20$ million, or as a decimal, $2.05$ , corresponding to an approximate $105$ percent increase in population for this age group.

For the $70 - 79$ year age group, the ratio is approximately $31$ million to $16$ million, or as a decimal, approximately $1.94$ , corresponding to an approximate $94$ percent increase in population for this age group.

Therefore, the $60 - 69$ year age group has the greatest projected percent increase in population from $2000$ to $2050$ among the given options.

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Subject Test Math 1

Question 27 of 32

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