How to write an exponential function given 2 points

One Point on the X-axis If one of the x-values -- say x1 -- is 0, the operation becomes very simple. Because the x-value of the first point is zero, we can easily find a.

In general, you have to solve this pair of equations: For example, solving the equation for the points 0, 2 and 2, 4 yields: Neither Point on the X-axis If neither x-value is zero, solving the pair of equations is slightly more cumbersome. From a Pair of Points to a Graph Any point on a two-dimensional graph can be represented by two numbers, which are usually written in the in the form x, ywhere x defines the horizontal distance from the origin and y represents the vertical distance.

Why Exponential Functions Are Important Many important systems follow exponential patterns of growth and decay. 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.

Plugging this value, along with those of the second point, into the general exponential equation produces 6.

On the other hand, the point -2, -3 is two units to the left of the y-axis. This yields the following pair of equations: Henochmath walks us through an easy example to clarify this procedure. If neither point has a zero x-value, the process for solving for x and y is a tad more complicated.

For example, the point 2, 3 is two units to the right of the y-axis and three units above the x-axis. The procedure is easier if the x-value for one of the points is 0, which means the point is on the y-axis.

Taking as the starting point, this gives the pair of points 0, 1. In his example, he chose the pair of points 2, 3 and 4, An Example from the Real World Sincehuman 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 this form, the math looks a little complicated, but it looks less so after you have done a few examples. How to Find an Exponential Equation With Two Points By Chris Deziel; Updated March 13, If you know two points that fall on a particular exponential curve, you can define the curve by solving the general exponential function using those points.

Inthe world population was 1. By taking data and plotting a curve, scientists are in a better position to make predictions.

For example, the number of bacteria in a colony usually increases exponentially, and ambient radiation in the atmosphere following a nuclear event usually decreases exponentially. You can substitute this value for b in either equation to get a.Feb 27,  · The points are (2,18) and (3,) in y=ab^x your a is your starting point and b is your growth factor.

To find b you have to find 18 times what gives you Status: Resolved. Just plug in the two sets of values for x and y (= f(x)) to obtain two equations. Divide one equation by the other to get the answer.

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– Mick Dec 30 '14 at If you know two points that fall on a particular exponential curve, you can define the curve by solving the general exponential function using those points. In practice, this means substituting the points for y and x in the equation y = ab x.

How to Find an Exponential Equation With Two Points

10 ab 3 Finding an Exponential Equation with Two Points and an Asymptote Find an exponential function that passes through (3,) and (4,) and has a horizontal asymptote of y = 4. Write an exponential function of the form y=ab^x whose graph passes through the given points.

(1,4),(2,12)The form is y = ab^x 12 = ab^2 4 = ab^Divide the 1st by the 2nd to get: 3 = bSubstitute that into the 2nd equation to solve for "a": 4 = a*3^1 a=(4/3)EQUATION: y = (4/3)*2^x ===== Cheers, Stan H.

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How to write an exponential function given 2 points
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