JJacquelin JJacquelin 60k 2 2 gold badges 30 30 silver badges 76 76 bronze badges. Since the equations are not linear, you have to use some numerical method of solving, generally involving initial guess and iterative process generalized Newton-Raphson or others. Search on the web for more information. It is only possible to optimise the three parameters so that the curve pass close to the four points.
This is a so called "regression" problem. Search on the web with key words "regression" and "fitting". I just want to know the best and easiest way to add the additional parameter. Show 1 more comment. EDIT: Suppose that we only want an exponential function. What is the general form you are looking for? Assuming you agree with my definition of exponential function, in general there is no exponential function that will fit four points.
Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. Upcoming Events. Featured on Meta. Now live: A fully responsive profile. In , wolves were counted. By the population had reached wolves. What two points can be used to derive an exponential equation modeling this situation?
Write the equation representing the population N of wolves over time t. Use the first equation to solve for a in terms of b :. Substitute a in the second equation, and solve for b :. Use the value of b in the first equation to solve for the value of a :. We can graph our model to check our work. The graph is an example of an exponential decay function. Figure 4. Do two points always determine a unique exponential function? Yes, provided the two points are either both above the x-axis or both below the x-axis and have different x-coordinates.
But keep in mind that we also need to know that the graph is, in fact, an exponential function. Not every graph that looks exponential really is exponential. We need to know the graph is based on a model that shows the same percent growth with each unit increase in x , which in many real world cases involves time.
Follow the guidelines above. Next, in the L1 column, enter the x -coordinates, 2 and 5. Do the same in the L2 column for the y -coordinates, Use a graphing calculator to find the exponential equation that includes the points 3, Skip to main content. Henochmath walks us through an easy example to clarify this procedure. In his example, he chose the pair of points 2, 3 and 4, This yields the following pair of equations:.
You can substitute this value for b in either equation to get a. It's easier to use the second equation, so:. Since , human population growth has been exponential, and by plotting a growth curve, scientists are in a better position to predict and plan for the future. In , the world population was 1.
Taking as the starting point, this gives the pair of points 0, 1. Because the x-value of the first point is zero, we can easily find a. Plugging this value, along with those of the second point, into the general exponential equation produces 6. Although it takes more than a slide rule to do it, scientists can use this equation to project future population numbers to help politicians in the present to create appropriate policies.
Chris Deziel holds a Bachelor's degree in physics and a Master's degree in Humanities, He has taught science, math and English at the university level, both in his native Canada and in Japan.
He began writing online in , offering information in scientific, cultural and practical topics.
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