Final answer:
To determine an exponential function from two points, log transform the y-values to linearize the equation and solve for 'a' and 'b'. Use a calculator's 'exp' and 'ln' functions if there's no direct exponent function available, and remember to square the exponent for squaring exponential terms.
Step-by-step explanation:
To determine the exponential function from two points using a calculator, you need to understand the relationship between the exponential function and its inverse function, the natural logarithm. Given two points (x1, y1) and (x2, y2), you can calculate the growth rate and initial value necessary for your exponential function, which is generally of the form y = abx.
First, let's use the natural logarithm to transform the exponential equation into a linear one: ln(y) = ln(a) + bx. If you solve this system using the two given points, you can find 'a' and 'b'. Often, this might require the use of a calculator that has an exponential 'exp' and a logarithm 'ln' function. Note that depending on your calculator, if it doesn't have a 'y*' button, you can still use 'ln' and 'exp' to find the values.
For instance, let's say your two points are (1, 2) and (3, 8). You would first take the natural log of the y-values: ln(2) and ln(8). These would give you two equations that can be solved for 'a' and 'b', helping you to find the specific exponential equation that passes through your points.
Remember to square the exponent when squaring exponential terms. Also keep in mind that points chosen for this should be far apart to accurately describe the function's slope. Once you have 'a' and 'b', you can write the exponential function and use it for further calculations, such as evaluating growth over a certain period or representing data on a graph with a best-fit exponential line.