Final answer:
The exponential equation to model the growth of the minimum wage in New York State from 1966 to 2015 can be determined using the exponential growth formula by plugging in the initial wage, the growth rate (which we solve for), and the number of years passed. Once the growth rate is found, it can be rounded to the nearest hundredth and matched with the answer options.
Step-by-step explanation:
To algebraically determine the exponential equation that models the growth of the minimum wage in New York State from $1.25 in 1966 to $8.75 in 2015, we use the formula of exponential growth:
Minimum Wage = Initial Wage × (1 + Growth Rate)^t
where:
- Initial Wage is the minimum wage in the starting year, which is $1.25.
- Growth Rate is what we need to find.
- t is the number of years since the starting year, which is 2015 - 1966 = 49 years.
Given the two minimum wages:
- In 1966, the minimum wage was $1.25.
- In 2015, the minimum wage was $8.75.
Using these values and the exponential growth formula, we have:
$8.75 = $1.25 × (1 + Growth Rate)^{49}
To solve for the Growth Rate, we divide both sides by $1.25, and then take the 49th root:
Growth Rate = (((8.75 / 1.25)^(1/49)) - 1)
After solving, we find the Growth Rate to the nearest hundredth. We then compare the calculated Growth Rate with the options provided. The correct Growth Rate will make the equation true for the values given for 1966 and 2015.