In 1950 the number of retirees was approximately 150 per thousand people aged 20-64. In 1990 this number rose to approximately 200, and it is projected to rise to 275 in 2020. Model N as a piecewise linear function of the time t in years since 1950, and use your model to project the number of retires per thousand people aged 20-64 in 1965. (Round you answer to the nearest integer.)
A)169 people per thousand
B) 219 people per thousand
C) 203 people per thousand
D) 152 people per thousand
E) 118 people per thousand

Question

In 1950 the number of retirees was approximately 150 per thousand people aged 20-64. In 1990 this number rose to approximately 200, and it is projected to rise to 275 in 2020. Model ​N as a piecewise linear function of the time t in years since 1950, and use your model to project the number of retires per thousand people aged 20-64 in 1965. (Round you answer to the nearest integer.) ​
A)169 people per thousand
B) 219 people per thousand
C) 203 people per thousand
D) 152 people per thousand
E) 118 people per thousand

Quizplus · Accepted Answer

To model $N$ as a piecewise linear function, we first find the slopes for each interval. From 1950 to 1990 (40 years), the number of retirees per thousand increased from 150 to 200, a change of 50 over 40 years, giving a slope of $50/40 = 1.25$ retirees per year. From 1990 to 2020 (30 years), it is projected to increase from 200 to 275, a change of 75 over 30 years, giving a slope of $75/30 = 2.5$ retirees per year. For 1965, 15 years after 1950, we use the first slope: $150 + 1.25(15) = 150 + 18.75 = 168.75$, which rounds to 169 retirees per thousand.

In 1950 the Number of Retirees Was Approximately 150 Per