# How to write an exponential function that passes through points

When multiplying reciprocals the answer is always a 1! 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.

And since multiplication is Commutative, we can do these operations in any order we choose! Then we will finish with a reciprocal: Dividing both sides by 4 we get: The -1 as an exponent tells us that a reciprocal will be found.

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.

Factoring our exponent this way we get: Henochmath walks us through an easy example to clarify this procedure. Plugging this value, along with those of the second point, into the general exponential equation produces 6.

Next we need to find a way to change the exponent on "b" to a 1. Why Exponential Functions Are Important Many important systems follow exponential patterns of growth and decay. Taking as the starting point, this gives the pair of points 0, 1. So now we have: Neither Point on the X-axis If neither x-value is zero, solving the pair of equations is slightly more cumbersome.

By taking data and plotting a curve, scientists are in a better position to make predictions. Because the x-value of the first point is zero, we can easily find a.

This yields the following pair of equations: The procedure is easier if the x-value for one of the points is 0, which means the point is on the y-axis.

Since finding a square root of 25 seems easier than the reciprocal, I choose to start with that. On the other hand, the point -2, -3 is two units to the left of the y-axis. On the right side we get or "b" just as we planned.

For example, solving the equation for the points 0, 2 and 2, 4 yields: One Point on the X-axis If one of the x-values -- say x1 -- is 0, the operation becomes very simple.

All we have to do is simplify the left side. 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.

If the exponent is fractional and the numerator is not a 1, factor out the numerator, For example, factor an exponent like into. 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.

If the graph passes through -2, then when we use an input of -2 for the function we should get as the output.

In this form, the math looks a little complicated, but it looks less so after you have done a few examples. If the exponent is negative, factor out a Raising a power to a power means we will multiply the exponents. The reasons we do this are: If neither point has a zero x-value, the process for solving for x and y is a tad more complicated.

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.Data Points and Exponential Functions So the exponential function that passes through the two data points is!

formula for the growth factor mentioned at the beginning of this document. Example (2) Is there an exponential function that passes through the three points given in.

Finding an Exponential Equation with Two Points and an Asymptote Find an exponential function whose asymptote is y=0 and passes through the points (2,16) and (6,). 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.

Find an exponential function that passes through the points $\left(-2,6\right)$ and $\left(2,1\right)$. Solution Because we donâ€™t have the initial value, we substitute both points into an equation of the form $f\left(x\right)=a{b}^{x}$, and then solve the system for a and b.

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6. Write an exponential function in the form y=ab^x whose graph passes through the given points: (2,48),(5,). Get an answer for 'Write an exponential function whose graph passes through the given points: (0, -2), and (-2, )' and find homework help for other Math questions at eNotes.

How to write an exponential function that passes through points
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