Question

Question #a73a3

Answer 1

Answer: `y = 0.25 * (1.0485)^t`

The exponential function will be `y=a*b^t`, where `a` is the initial value

So, `a=0.25` because the hourly minimum wage has the initial value of `$0.25` at the moment `t=0` (the year 1938).

(Verification: for `t=0`, `y=0.25*b^0` `=` `0.25*1 =0.25`)

In 2009, after 71 years, the value of the hourly minimum wage is $7.25. Therefore, `y=7.25` for `t=71`.

So, **`7.25=0.25*b^71` **

In order to find our exponential function, we have to find the value of `b`.

`b^71=7.25 / 0.25` `= 29` `=>` `b=root71(29)` `~~1.0485`

Hence, our exponential function is `y=0.25*(1.0485)^t`

Based on this model, we can estimate the values of the hourly minimum wage for the other years, by substituting the values of `t` in the general formula:

• for 2015, `t=77` `=>` `y=0.25*(1.0485)^77~~9.5875`
• for 2016, `t=78` `=>` `y=0.25 * (1.0485)^78~~10.0525`

This is the graph of the function: