Building on the analytical and leadership skills developed in your Math class, you run a successful small business for 2 years. After selling the business, you purchase a new car for $55000. The value of the car after $\displaystyle {t}$ years is given by the function

$\displaystyle {V}{\left({t}\right)}={55000}{\left({0.55}\right)}^{{t}}$

where $\displaystyle {t}$ is the number of years after the purchase and $\displaystyle {V}{\left({t}\right)}$ is the value of the car in dollars.

Determine $\displaystyle {V}{\left({3}\right)}$.

$\displaystyle {V}{\left({3}\right)}=$Preview Question 6 Part 1 of 6  


Interpret the meaning of $\displaystyle {V}{\left({9}\right)}={253}$.

Select an answer The value of the car 2 years after purchase is $16638. The value of the car 9 years after purchase is $253. The value of the car 2 years after purchase is depreciating $16638 per year. The value of the car 9 years after purchase is depreciating $253 per year. The value of the car 16638 years after purchase is $9.


Determine $\displaystyle {V}'{\left({t}\right)}$.

$\displaystyle {V}'{\left({t}\right)}=$Preview Question 6 Part 3 of 6  


Determine $\displaystyle {V}'{\left({3}\right)}$.

$\displaystyle {V}'{\left({3}\right)}=$Preview Question 6 Part 4 of 6  


Interpret the meaning of $\displaystyle {V}'{\left({9}\right)}=-{9947}$.

Select an answer The value of the car 9 years after purchase is $16638. The value of the car 9 years after puchase is depreciating $9947 per year. The value of the car 9 years after purchase is depreciating $253 per year. The value of the car 9 years after purchase is -$9947. The value of the car 2 years after purchase is depreciating $9947 per year.


Explain how the value of $\displaystyle {V}'{\left({1}\right)}=-{18085}$ might affect your decision to buy a new car.