1. ## Word problem involving derivatives. Need answers!

The value of an automobile purchased in 2007 can be aproximated by the function V(t)= 25(0.85)^t,
where t is the time, in years, from the date of purchase, and V(t) is the value, in thousands of dollars.

a.) Evaluate and interpret V(4)

b.) Find an expression for the derivative of V(t), including units.

c.) Evaluate and interpret V'(4)

d.) Use V(t) and V'(t), and any other considerations you think are relevant to write a paragraph in support of or in opposition to the following statement:
"From a monetary point of view, it is best to keep this vehicle as long as possible."

I really want to see feedbacks for question d, so please explain it in details. Thank you!

2. ## Re: Word problem involving derivatives. Need answers!

Hey Mathinik.

We know that if something has a negative derivative it means it's decreasing. What can you say about the derivative for t > 0 and what can you conclude about the value in the long term given this information?

3. ## Re: Word problem involving derivatives. Need answers!

Chiro,

I still don't get it!

4. ## Re: Word problem involving derivatives. Need answers!

If something is continually decreasing (i.e always getting smaller) what does that mean about the value? What does this imply later in the future (if it's decreasing, will it be worth a lot less or a lot more)?

5. ## Re: Word problem involving derivatives. Need answers!

It's getting cheaper each year. It will be worth a lot less. So it is best to not keep this vehicle as long as possible?

7. ## Re: Word problem involving derivatives. Need answers!

need help still

8. ## Re: Word problem involving derivatives. Need answers!

You're not going to get answers. You are going to use the guidance given by the members here to come to the answers YOURSELF. Also, I don't see how your original function can possibly have been written correctly. You would expect a car's value to decrease over time, but what you have written is an INCREASING function.