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 2003. (Round you answer to the nearest integer.)

a. 163 people per thousand

b. 279 people per thousand

c. 302 people per thousand

d. 209 people per thousand

e. 233 people per thousand

Answer: 233 people per thousand

Step-by-step explanation:

Using extrapolation method,

if 150/k in 1950,

200/k in 1990,

275/k in 2020,

2003 lies in between 1990 and 2020. So, you extrapolate the values of 200/k and 275/k for the years respectively.

Therefore,

(2003 - 1990) / (2020 - 2003) = (x - 200) / (275 - x)

Where x is the number of retirees per thousand for 2003

Making x the subject of relation in the above equation.

Cross multiply the equation above;

(2003 - 1990) (275-x) = (2020 - 2003) (x - 200)

13 (275 - x) = 17 (x-200)

3575 - 13x = 17x - 3400

Collect the like terms

3575+3400 = 17x + 13x

30x = 6975

x = 6975/30

x = 232.5

x = 233 people per thousand to the nearest integer