Assume that in one country in 2005, 12.9 % of the population was 65 or older. By
ID: 3196714 • Letter: A
Question
Assume that in one country in 2005, 12.9 % of the population was 65 or older. By 2050, this percent is expected to be 21.54%. The percent of the population ages 25-34 in 2005 was 13.9%. That age group is expected to include 13.1035% of the population in 2050.
a. Assuming these population changes are linear, use the data for the 65 or over age group to write a linear equation. Then do the same for the25-34 age group. Let
xequals=0
represent 2005 and
xequals=45
represent 2050. Express percents in decimal form.
For the population of 65 or older the equation is
yequals=nothing.
For the population of 25-34 years the equation is
yequals=nothing.
b. Solve the system of linear equations from part (a). In what year will the two age groups include the same percent of the population? What is that percent?
The age groups include the same percent of population in the year
nothing.
(Do not round until the final answer. Then round to the nearest year as needed.)
The percent is
nothing%.
(Do not round until the final answer. Then round to the nearest tenth as needed.)
Explanation / Answer
The growth is linear.
For age group 65or older
y=mx + c
When x=0,y=12.9%
Substituting we get c=12.9
When x=45,y=21.54%
Substituting we get m=0.192
y = 0.192x + 12.9
For age group 25-34
y=mx+c
When x=0, y=13.9%
Substituting we get c=13.9
When x=45,y=13.1035
Substituting we get m = - 0.0177
y = - 0.0177x + 13.9
A) When population percents are equal:
This implies that: 0.192x + 12.9 = - 0.0177x + 13.9
Solving we get x = 4.76872 which means year 2010
Population percent = 0.192*4.76872 + 12.9 = 13.81559% = 13.8%