Exponential and Logarithmic Functions

e
This file has five sheets. The first shows how the value for e is derived from the binomial series for (1+x)ⁿ and this is used on the second sheet to derive the series for ex. The third sheet finds the derivative of e^x. The next two sheets explore the relationship between the total interest generated and the number of times compound interest is added to an investment. The final sheet investigates the area under the graph of ¹/_x and derives the integral of ¹/_x.

Logarithms
This begins with a sheet listing the values of an and the value of log_n where n can be altered. The second sheet uses the base e and introduces natural logarithms. The next two sheets require students to estimate the values of logarithms to different bases from the graphs shown. The fourth sheet illustrates the exponential and logarithmic functions on one graph where different bases can be selected. Subsequent sheets deal with the sum and difference of logs, the log of alog_x, and changing the base of logarithms. The final two sheets generate questions where students need to evaluate logs and answer questions based on the laws derived in the previous sheets. Answers can be revealed and new sets of questions generated.

Exponential and Logarithmic Functions
The first two sheets explore the graphs of exponential functions. The base can be altered and the appropriate graphs shown. Negative exponents are also explored and the relationship between the graphs of a^x and a^-x illustrated. The third sheet explores the graph of e^kx and the relationship between the value of the function and its gradient. The next two sheets show the derivation of the value of e as a limit and the sum of the series. The final sheet shows the graphs of exponential functions together with the inverse logarithmic functions.

Note: This program was designed by be viewed on a screen with a resolution of 1024 x 768. Users may have to adjust the resolution of their screen for the pages to display as was originally intended. The program uses macros which need to be enabled on users’ machine.