In 1968 the US minimum wage was 160 per hour In 1974 the min

In 1968, the U.S. minimum wage was $1.60 per hour. In 1974, the minimum wage was $2.00 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). (Round values to three decimal places.)

Solution

1968----minimum wage was $1.60 per hour

1974---- the minimum wage was $2.00 per hour.

Let W variable defines wages;

W= Woe^(kt) where k is a exponential factor

Base year ---1960.

So 1968------ 08 years ---- $ 1.60per hr

1974 ----- 14 years -------$ 2.00 per hr

Substituting these values in the exponential equation to get Wo and k

1.60 = Woe^(8k)

2.00 = Woe^(14k)

Divide both equations we get : 2/1.6 = e^(6k)

Taking natural log of both sides: ln(1.25) = 6k

k =0.037

Now find Wo: 1.6 = Woe^(0.037*8)

Wo= $1.19 per hour

W = 1.19e^(0.037t)