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To find an exponential function through two given points, one can use the properties of exponential functions. An exponential function is typically in the form y = ab^x. By substituting the coordinates of the two points into this equation, a system of linear equations can be formed to solve for the constants a and b. Alternatively, on calculators like Ti83 or Ti84, the exponential regression function (fx-abx) can be utilized to quickly find the exponential equation that best fits the given data points, even if the initial value is not explicitly given.

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