Problem

Junker Renovation completely overhauls junked or abandoned cars. Data shows their 1970's models hold their value quite well. The value $F(x)$ of one of these cars is given by $F(x)=70-\frac{14 x}{x+1}$, where $x$ is the number of years since repurchase and $F$ is in hundreds of dollars. Step 1 of 3 : What is the initial resale price of the car?

Solution

Step 1 :Junker Renovation completely overhauls junked or abandoned cars. Data shows their 1970's models hold their value quite well. The value $F(x)$ of one of these cars is given by $F(x)=70-\frac{14 x}{x+1}$, where $x$ is the number of years since repurchase and $F$ is in hundreds of dollars.

Step 2 :The initial resale price of the car is the value of the car when $x=0$, which is when the car is repurchased. So, we need to substitute $x=0$ into the function $F(x)$ to find the initial resale price.

Step 3 :Substituting $x=0$ into the function $F(x)$, we get $F(0)=70-\frac{14 \times 0}{0+1}=70$

Step 4 :Final Answer: The initial resale price of the car is \(\boxed{70}\) hundreds of dollars, or \(\boxed{7000}\) dollars.

From Solvely APP
Source: https://solvelyapp.com/problems/17702/

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