Exponential Model of growth of Minimum Wage

Question

In 1968, the US minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30 per hour. Assume the minimum wage grows according to an exponential model w(t), where t represents the time in years after 1960.

a) Find a formula for w(t)

b) What does the model predict for the minimum wage in 1960?

c) If the minimum wage was $5.15 in 1996, is this above, below, or equal to what the model predicts?

 

Answer 1

t = year - 1960

exponential model y = ab^x

1.60 = ab^8 = minimum wage in 1968

2.30 = ab^18 = min wage in 1976

divide 1st into 2nd equation to get

23/16 = b^10

b = 10th root of 23/10 = about 1.04

2.3= a(1.036957)^18 =

a= about .83258

model is

minimum wage = .83258(1.037)^t

in 1960, min wage = .about .83(1.037)^0 = about 83 cents per hour

in 1996 min wage = $5.15 how close was the model's prediction?

= .83(1.037)^36 = about $3.08 off by $2.07

model didn't take account of unexpected inflation