Results 1 to 8 of 8

Math Help - Growth rate

  1. #1
    Member
    Joined
    Oct 2012
    From
    Nowhere
    Posts
    82

    Growth rate

    Suppose that the number of cell phones in the world increases by a total of 160% over a five-year period. What is the continuous growth rate for the number of cell phones in the world?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    4,163
    Thanks
    761

    Re: Growth rate

    Hey Eraser147.

    Continuous growth is exponential where you are looking at A*e(bx) for constant A and b. You need two values to solve for two independent equations but you know f(x+5) = 1.6*f(x) for some particular value of x and you can cancel A from both sides.

    Can you use this to solve for b?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Oct 2012
    From
    Nowhere
    Posts
    82

    Re: Growth rate

    1.6(x+5) = 1.6x+8? b=8??
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    4,163
    Thanks
    761

    Re: Growth rate

    No, f(x) is a function: f(x) = Ae^(bx) where f(x+5) = Ae^(b[x+5]).

    You are not multiplying a constant f by x: f is a function that takes a value for x and spits out a value called f(x).

    1.6*f(x+5) = 1.6*A*e(b[x+5]) = 1.6Ae^[bx + 5b] = 1.6Ae^[bx]*e^[5b] = f(x).
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Oct 2012
    From
    Nowhere
    Posts
    82

    Re: Growth rate

    Sorry, but I really don't know where to go from 1.6Ae^[bx]*e^[5b] = f(x). Can you please show me the whole entire solution. I think that would help me trace out everything that you are trying to tell me.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    4,163
    Thanks
    761

    Re: Growth rate

    What does f(x) equal? (Hint: I posted it above, just plug it in).
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Oct 2012
    From
    Nowhere
    Posts
    82

    Re: Growth rate

    Well, I just figured it out this way which was similar to my student's solution manual.. If the initial amount was 0, then... if it raised up to 160%, that means that it went up 2.6 times the original number. Then I can have this formula 2.6P=Pe^5r which is ln2.6/5
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    4,163
    Thanks
    761

    Re: Growth rate

    Yes sorry I made a mistake in that you should have 2.6f(x+5) = f(x). If you cancel out the A and e^(bx) from both sides you will get exactly the same equation as in the solution manual.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: August 11th 2012, 02:22 PM
  2. Growth Rate
    Posted in the Algebra Forum
    Replies: 1
    Last Post: May 26th 2010, 02:03 AM
  3. Rate of Growth
    Posted in the Calculus Forum
    Replies: 9
    Last Post: February 22nd 2010, 10:14 PM
  4. Replies: 2
    Last Post: October 15th 2009, 07:06 AM
  5. Growth rate
    Posted in the Business Math Forum
    Replies: 4
    Last Post: May 27th 2009, 11:05 PM

Search Tags


/mathhelpforum @mathhelpforum