Question

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?

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