Chapter 5.2, Problem 79E

Monthly Payment The model

$\begin{array}{l}t=\text{16}\text{.625 ln}\frac{x}{x-750},x>750\\ \end{array}$

approximates the length of a home mortgage of $\text{\$}150,000$ at $6\text{\%}$ in terms of the monthly payment. In the model, $t$ is the length of the mortgage in years and $x$ is the monthly payment in dollars.

(a). Approximate the lengths of a $\text{\$}150,000$ mortgage at $6\text{\%}$ when the monthly payment is

$\text{\$}897.72$ and when the monthly payment is $\text{\$}1659.24$.

(b). Approximate the total amounts paid over the term of the mortgage with a monthly

payment of $\text{\$}897.72$ and with a monthly payment of $\text{\$}1659.24$. What amount of the total

is interest costs in each case?

(c). What is the vertical asymptote for the model? Interpret its meaning in the context of the

problem.