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Math Help - Instantaneous rate

  1. #1
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    Instantaneous rate

    I need to know how to estimate the instantaneous rate of population growth of a month. In the previous question i was asked to find the average rare of population growth which i believe would be to just find the slope. ( Is that correct?

    In order to find the instantaneous rate of population growth of a month I believe you have to find the slope of the tangent line. so do I just find a tangent line and estimate to coordinates and use the slope fomula?

    When i did this i got a fraction of 70/8. Can ths slope be a fracton when it comes to population growth?
    Last edited by asweet1; November 8th 2009 at 01:58 PM. Reason: did problem need feedback
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  2. #2
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    Quote Originally Posted by asweet1 View Post
    I need to know how to estimate the instantaneous rate of population growth of a month. In the previous question i was asked to find the average rare of population growth which i believe would be to just find the slope. ( Is that correct?

    In order to find the instantaneous rate of population growth of a month I believe you have to find the slope of the tangent line. so do I just find a tangent line and estimate to coordinates and use the slope fomula?

    When i did this i got a fraction of 70/8. Can ths slope be a fracton when it comes to population growth?
    what are you working with, a table of values?

    how did you arrive at 70/8 ? more problem info, please.
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  3. #3
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    Quote Originally Posted by asweet1 View Post
    I need to know how to estimate the instantaneous rate of population growth of a month. In the previous question i was asked to find the average rare of population growth which i believe would be to just find the slope. ( Is that correct?

    In order to find the instantaneous rate of population growth of a month I believe you have to find the slope of the tangent line so do I just find a tangent line and estimate to coordinates and use the slope fomula?

    When i did this i go a fraction of 70/8. Can ths slope be a fracton when it comes to population growth?
    Yes, you are correct about the instantaneous rate. That's just the derivative. I'm not sure what you're asking after that (in red). I assume you have a population growth curve of some kind. If you want to approximate the slope of a tangent line around a certain point (x,y) then just find the slope of the secant line which passes through two points near the point (x,y) on the curve.
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  4. #4
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    So once i find the slope of the secant line how do i incororate it into the tangent line coordinates i found?
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  5. #5
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    To skeeter i am working with a graph i got 70/8 by finding p'(22)= p(22)-P(14)/22-14 which equals to 380-310/22-14
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    Quote Originally Posted by asweet1 View Post
    So once i find the slope of the secant line how do i incororate it into the tangent line coordinates i found?
    I'm not sure what you mean by 'tangent line coordinates.' A tangent line is represented by an equation \Delta y=y'\Delta x. It's not represented by a pair of coordinates. I think you may be referring to the point of tangency.

    Could you provide the exact wording of the problem you're working on? What is the function?
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  7. #7
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    A small lake is stocked with trout in the early sprin of 2005. The population of trout in the lake (where t is measured in months) is shown below. (it shows a graph)

    (a) what is the average rate of population growth bewtween month 10 and month 20?

    -Here i would find the slope

    (b) Estimate the instantaneous rate of population growth month 22.

    -Here i am not sure what to do exactly
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  8. #8
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    It's not easy to help without the graph. But I'll give you a brief tip.

    Find two points, one on each side, of the point at t=22 months. Chose the points so that they are very close to the point at t=22 months. Draw a line through these points. The equation of the line through the points will be the approximation you're looking for.
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