# Question a73a3

May 21, 2015

Answer: $y = 0.25 \cdot {\left(1.0485\right)}^{t}$

The exponential function will be $y = a \cdot {b}^{t}$, 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 \cdot {b}^{0}$$=$$0.25 \cdot 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, $7.25 = 0.25 \cdot {b}^{71}$

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

${b}^{71} = \frac{7.25}{0.25}$ $= 29$ $\implies$ $b = \sqrt[71]{29}$ $\approx 1.0485$

Hence, our exponential function is $y = 0.25 \cdot {\left(1.0485\right)}^{t}$

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, $t = 77$ $\implies$ $y = 0.25 \cdot {\left(1.0485\right)}^{77} \approx 9.5875$
• for 2016, $t = 78$ $\implies$ $y = 0.25 \cdot {\left(1.0485\right)}^{78} \approx 10.0525$

This is the graph of the function: