Can anyone help me with this math problem?!

Question

the number of workers per Social Security beneficiary has been declining approximately linearly since 1970. in 1970 there were 3.7 workers per beneficiary. in 2050 it is projected there will be 2.0 workers per beneficiary. let W be the workers per Social Security beneficiary and t be the number of years since 1970. a) find a function W(t) that fits the data b) estimate the number of workers per beneficiary in 2020.

Answer 1

(a)

 

You seek an equation of the form

 

W(t) = at + b,

 

where a and b are constants.

 

t = 0 is year 1970

 

You have 2 points to work with:

 

1970:  (t₁,W₁) = (0,3.7)

2050:  (t₂,W₂) = (80,2.0)  [2050 is 80 years after 1970]

 

a = ΔW/Δt = (2.0 - 3.7) / (80 - 0) = -1.7/80 = -0.02125

 

W(t) = -0.02125t + b

 

Get b from either point.  Using (0,3.7),

 

3.7 = -0.02125(0) + b

b = 3.7

 

Final equation:

 

W(t) = -0.02125t + 3.7

 

You can test it at both points.

 

(b)

 

At 2020, t = 50 years since 1970

 

W(50) = -0.02125(50) + 3.7 = 2.6375