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Harrisonized said:
It might be instructive to plot the raw data on semilog graph paper. (Search on google, and print out a sheet of it.) The curve of best fit should be a straight line. Measure its slope. From this you can work out the equation you seek. This should support the figures in the right-most column of your data. This exercise amounts to graphically taking an average of the numbers in the right column, and, if it hadn't already been done, would save calculating those numbers.schan11 said:
An exponential function is a mathematical function in the form of f(x) = a^x, where a is a constant and x is the variable. This means that the value of the function increases or decreases at a constant rate as x increases, resulting in a curved graph.
To solve an exponential function, you can use logarithms or graphing techniques. If using logarithms, you take the logarithm of both sides of the equation and then solve for x. If using graphing techniques, you plot points on a graph and use the points to create a line of best fit that represents the exponential function.
Exponential functions are commonly used in various fields such as finance, biology, and physics. In finance, they are used to model compound interest and growth of investments. In biology, they can be used to model population growth. In physics, they are used to model radioactive decay and other natural phenomena.
To graph an exponential function, you can use the points method or the transformations method. The points method involves choosing values for x and solving for the corresponding values of y. The transformations method involves applying transformations such as horizontal and vertical shifts, reflections, and stretches to the parent function y = a^x.
The main difference between exponential and linear functions is that exponential functions have a variable in the exponent while linear functions have a variable raised to the first power. This results in exponential functions having a curved graph while linear functions have a straight line graph. Additionally, exponential functions have a constant rate of change while linear functions have a constant slope.
