Question

In New York State, the minimum wage has grownexponentially. In 1966, the minimum wage was$1.25 an hour and in 2015, it was $8.75.Algebraically determine the rate of growth to thenearest percent.

Answer 1

The Solution.

In 1966, which is the initial year(t); t = 0, and minimum wage(y), y = $1.25

Similarly.

In 2015, t = 49 years , (that is, 1966 to 2015), and y = $8.75

The rate of growth to the nearest percent is

$\text{Rate of growth =}\frac{y_2-y_1}{t_2-t_1}\times100$$\begin{gathered} \text{Where y}_2=8.75,t_2=49\text{ years} \\ y_1=\text{ \ 1.25},t_1=0 \end{gathered}$

Substituting into the formula above, we get

$\text{Rate of growth =}\frac{8.75-1.25}{49-0}\times100$$\text{Rate of growth = }\frac{7.5}{49}\times100=15.31\approx15\text{ \%}$

Hence, the correct answer is 15%