Final answer:
To find an exponential function passing through given points with a graphing calculator, transform the exponential function to a linear form by taking the natural logarithm, perform linear regression, and then convert back to exponential form.
Step-by-step explanation:
To find an exponential function that passes through given points, you can use a graphing calculator such as the TI-83, 83+, or 84. This task involves solving a system of linear equations that derive from the exponential model.
Given two points, (x1, y1) and (x2, y2), one can assume the exponential function to be of the form y = abx. Taking the natural logarithm of both sides of the equation gives ln(y) = ln(abx), which simplifies to ln(y) = ln(a) + x ln(b). The transformed equation resembles a linear equation y = mx + c. Thus, by entering the ln-transformed y-values and the x-values into the calculator, you can obtain a linear regression model from which coefficients ln(a) and ln(b) can be calculated. The calculator will round the constants to four decimal places, providing an accurate model for your data.
Once you have these coefficients, you can find the original values of a and b by taking the exponential of the coefficients. That is, a = eln(a) and b = eln(b). The regression feature on the calculator will provide these values, completing the exponential model y = abx that passes through the given points.