1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Writing an Exponential Model

  1. Jan 7, 2012 #1
    1. The problem statement, all variables and given/known data

    A new car that costs $30,000 has a book value of $18,000 after 2 years.

    a) Find a linear model that represents the value 'V' of the care after 'x' years

    b) Find an exponential model of V= ab^(x) that represents the value 'V' of the car after 'x' years.

    2. Relevant equations


    3. The attempt at a solution

    I found the linear model just by basic graphing knowledge and using slope formula.

    Linear Model: V= -6,000x + 30,000

    I don't know how to find the exponential function, I know its a decay so it has to be a fraction, but how do I start it, and what is it supposed to be?
  2. jcsd
  3. Jan 7, 2012 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    When you did your linear model, you had an unknown equation ##y = mx + b##. You are probably familiar enough with that form that you knew the two unknowns are the slope and y intercept. If you hadn't known that, you would have plugged in the two points giving you two equations in two unknowns a and b.

    Do the exponential the same way. Plug in the two points to get two equations in two unknowns.
  4. Jan 7, 2012 #3
    What would I plug the points in to? I am getting confused with the variable 'a' and 'b' from y=ab^(x)

    This is my shot at what you said:

    I plugged the points (0,30000) in first and got 'a' to be 30000 then plugged that 'a' value into y=ab^x again, for the point (2,18000)



    18000= 30000*(b)^2
    18/30 = b^2

    then for the final equation to model the situation, I got this:

    V= 30000*((√15)/5)^x

    Would that be correct?
  5. Jan 7, 2012 #4


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    All you have to do to see if it is correct is to check whether it passes through your two points (0,30000) and (2,18000).
  6. Jan 7, 2012 #5
    oh yeah hahahah, I just remembered that while I was reading your post, lol sorry
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook