Question

The federal minimum wage was raised to $1.00 per hour in 1956. It was raised to $2.00 per hour in 1974. If it had continued to increase at this same exponential rate, what would it be in 2016?

I tried working this problem and got ~$10.08 for 2016. I'm not sure if my answer is correct however.
Any help is greatly appreciated!

Answer 1

assume that 1956 represents a time of t=0
and t is the number of years since 1956
so 1974 ---> t = 8
2016 ---> t = 60

If m is the minimum wage, then

m = 1 e^(kt)
when t = 8 , m = 2
2 = e^(8k)
8k = ln2
k = ln2/8

so m = e^( (ln2/8)t)
when t = 60
m = e^(60(ln2/8)) = 181.02

or

using the doubling formula
since it took 8 years to double
m = 2^(t/8)
so when t = 60
m = 2^(60/8)
= 2^7.5
= 181.02

Wow, better not let Trump and the other boys know about that.