We are given that the amount $37184 will increase by a percentage of 6% every year. This can be modeled using an equation of exponential growth, which follows the next function:
[tex]y=P_0(1+r)^t[/tex]Where:
[tex]\begin{gathered} P_0=\text{ initial value} \\ r=\text{ growth rate} \\ t=\text{ time} \end{gathered}[/tex]The initial value is:
[tex]P_0=37184[/tex]The growth rate must be in decimal form. To obtain the decimal form we divide the percentage rate by 100:
[tex]r=\frac{6}{100}=0.06[/tex]Now, we substitute the values:
[tex]y=37184(1+0.06^{})^t[/tex]Now, we solve the operations inside the parenthesis:
[tex]y=37184(1.06)^t[/tex]Now, we substitute the value of "t = 13", we get:
[tex]y=37184(1.06)^{13}[/tex]Solving the operations:
[tex]y=79311[/tex]Therefore, her salary in 13 years will be $79311
