We are given the following relationship:
[tex]y=2x+76[/tex]Where "y" is price and "x" is years. We are asked to find the number of years for the price to be $100. To do that, we will replace the value of "y" for 100, like this:
[tex]100=2x+76[/tex]Now, we will solve for "x", first by subtracting 76 on both sides:
[tex]\begin{gathered} 100-76=2x+76-76 \\ 24=2x \end{gathered}[/tex]Now we divide both sides by 2
[tex]\begin{gathered} \frac{24}{2}=\frac{2x}{2} \\ 12=x \end{gathered}[/tex]The value of "x" is 12, therefore, it is needed 12 years for the price to increase to $100.
