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In 1968, the U.S. 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.

Find the Formula for w(t)

My work so far:
n=y(not)
t=0
y=1.60

1.60=nb^0
n=1.6

t=8
y=2.30
2.30=1.60b^8
b=1.04640783

the final answer is suppose to be
y=1.113(1.04640783)^t
but i don't know how to find the 1.113
where did that come from?

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1 answer

  1. I see an error in your first calculation
    1960 ---> t = 0
    1968 ---> t = 8, you had t = 0

    so
    1.6 = a(b)^8
    2.3 = a(b)^16

    divide the second equation by the first
    1.4375 = b^8
    b = 1.0464678

    then in the first
    1.6 = a(1.0464678)^8
    1.6 = a(1.4375)
    a = 1.6/1.4375
    a = 1.11304

    so w(t) = 1.11304(1.0464678)^t

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