Question

The average price (in dollars) to rent a studio in a certain city can be approximated by the equation p = 25.5t + 645where t is the number of years since 1990. Solve this equation for t and use the new equation to determineapproximately what year it will be when the average price of a studio in this city reaches $1,385.

Answer 1

The first step is to solve this equation for t. To do this, we have to isolate t and bring p to the right side of the equation:

`\begin{gathered} p=25.5t+645 \\ -25.5t=-p+645 \\ t=(p)/(25.5)-(645)/(25.5) \\ t=0.0392p-25.2941 \end{gathered}`

We can now plug in p = 1385 and solve for t:

`\begin{gathered} t=0.0392(1385)-25.2941 \\ t=54.3137-25.2941 \\ t\approx29 \end{gathered}`

We know that t is the number of years AFTER 1990, so the year we are looking for is 1990 + t, which is 1990 + 29 or 2019